The sum of the measures of the interior angles of a polygon with n sides is (n – 2)180. A polygon is a closed geometric figure with a number of sides, angles and vertices. Since every triangle has interior angles measuring 180° 180 °, multiplying the number of dividing triangles times 180° 180 ° gives you the sum of the interior angles. [1] X Research source The value 180 comes from how many degrees are in a triangle. For example, if you know the number of sides of a polygon, you can figure out the sum of the interior angles. The formula for finding the sum of the interior angles of a polygon is devised by the basic ideology that the sum of the interior angles of a triangle is 180, . (n - 2) 180° (23 - 2)180° 21 x 180° 3780° A polygon with 23 sides has a total of 3780 degrees. The sum of all the internal angles of a simple polygon is 180 (n –2)° where n is the number of sides. A polygon will have the number of interior angles equal to the number of sides it has. Sum of interior angles of a polygon. The angle sum of this polygon for interior angles can be determined on multiplying the number of triangles by 180°. The sum of interior angles is \((6 - 2) \times 180 = 720^\circ\).. One interior angle is \(720 \div 6 = 120^\circ\).. The sum of the measures of the interior angles of a convex polygon with n aspects is $ (n2)a hundred and eighty^\circ $ examples triangle or ( '3gon'). The sum of interior angles of a regular polygon and irregular polygon examples is given below. The name of the polygon generally indicates the number of sides of the polygon. intelligent spider has proved that the sum of the exterior angles of an n-sided convex polygon = 360° Now, let us come back to our interior angles theorem. A series of images and videos raises questions about the formula n*180-360 describing the interior angle sum of a polygon, and then resolves these questions. Question 2: Find the measure of each interior angle of a regular decagon. Sum of interior angles of Quadrilaterals. Interior angle sum of polygons: a general formula Activity 1: Creating regular polygons with LOGO (Turtle) geometry. Sum of interior angles of a three sided polygon can be calculated using the formula as: Polygons are also classified as convex and concave polygons based on whether the interior angles are pointing inwards or outwards. Related Topics. Same thing for an octagon, we take the 900 from before and add another 180, (or another triangle), getting us 1,080 degrees. Pro Lite, CBSE Previous Year Question Paper for Class 10, CBSE Previous Year Question Paper for Class 12. Type your answer here… Check your answer. The sum of the interior angles of a polygon is given by the product of two less than the number of sides of the polygon and the sum of the interior angles of a triangle. So the sum of the polygon's angles is 180 n - 360, and what does that equal? To find the size of each interior angle of a regular polygon you need to find the sum of the interior angles first. Sum of interior angles of Hexagons. Polygons method for exterior angles and interior angles. Interior Angles of Polygons. Step 1: Count the number of sides and identify the polygon. At the point where any two adjacent sides of a polygon meet (vertex), the angle of separation is called the interior angle of the polygon. The Interior Angles of a Polygon (The Lesson) The interior angles of a polygon are the angles between two sides, inside the shape.. The formula can be obtained in three ways. If a polygon has ‘p’ sides, then. Type your answer here… Check your answer. An exterior angle of a polygon is made by extending only one of its sides, in the outward direction. Sum of Interior Angles Formula This formula allows you to mathematically divide any polygon into its minimum number of triangles. A regular polygon is both equilateral and … The number of triangles is always two less than the number of sides. Let's Review To determine the total sum of the interior angles, you need to multiply the number of triangles that form the shape by 180°. Though the sum of interior angles of a regular polygon and irregular polygon with the same number of sides the same, the measure of each interior angle differs. We can check this formula to see if it works out. Next lesson. Irregular polygons are the polygons with different lengths of sides. Now you say the sum of the interior angles is twice the sum of the exterior angles, that is, 720 deg, By drawing diagonals to the remaining vertices from any vertex, you form triangles. Polygon has 13 angles. An irregular polygon is a polygon with sides having different lengths. Your email address will not be published. Hence it is a plane geometric figure. For example the interior angles of a pentagon always add up to 540° no matter if it regular or irregular, convex or concave, or what size and shape it is. Sum of Interior Angles of a Polygon. In this formula, n is the number of sides of the polygon. In fact, the sum of ( the interior angle plus the exterior angle ) of any polygon always add up to 180 degrees. Step 1: Count the number of sides and identify the polygon. Whats people lookup in this blog: The point P chosen may not be on the vertex, side or inside the polygon. Hence, we can say now, if a convex polygon has n sides, then the sum of its interior angle is given by the following formula: S = ( n − 2) × 180° The formula is $sum\; =\; (n\; -\; 2)\; \backslash times\; 180$, where $sum$ is the sum of the interior angles of the polygon, and $n$ equals the number of sides in the polygon. Let us discuss the three different formulas in detail. the sum of the interior angles is: #color(blue)(S = 180(n-2))# Properties. Since, all the angles inside the polygons are same, therefore, the formula for finding the angles of a regular polygon is given by; Sum of interior angles = 180° * (n – 2) Where n = the number of sides of a polygon. Polygons have all kinds of neat properties! Find the number of sides in the polygon. An interior angle is located within the boundary of a polygon. A pentagon has 5 sides, and can be made from three triangles, so you know what ..... its interior angles add up to 3 × 180° = 540° And when it is regular (all angles the same), then each angle is 540° / 5 = 108° (Exercise: make sure each triangle here adds up to 180°, and check that the pentagon's interior angles … The sum of the internal angle and the external angle on the same vertex is 180°. Perspective sums nctm illuminations. 1. Identify the polygon below and determine the sum of the interior angles by using a formula. The Sum of the Interior Angles of a Polygon. The sum of all of the interior angles can be found using the formula S = (n - 2)*180. Activity 2: Investigating a general formula for the sum of the interior angles of polygons 1a) You may have earlier learnt the formula S = 180( n -2) by which to determine the interior angle sum of a polygon in degrees, but this formula is only valid for simple convex and concave polygons, and NOT valid for a star pentagon like the one shown below. There are different types of polygons based on the number of sides. A polygon with three sides is called a triangle, a polygon with 4 sides is a quadrilateral, a polygon with five sides is a pentagon, a polygon with 6 sides is a hexagon and so on. Sum of interior angles = 180(n – 2) where n = the number of sides in the polygon. Sum of all the interior angles of a polygon with ‘p’ sides is given as: Sum of Interior Angles of a Polygon Formula: The formula for finding the sum of the interior angles of a polygon is devised by the basic ideology that the sum of the interior angles of a triangle is 1800. 2. Sum of interior angles = 180(n – 2) where n = the number of sides in the polygon. For example, if you know the number of sides of a polygon, you can figure out the sum of the interior angles. Example: ... Pentagon. The sum of the measures of the interior angles of a polygon with n sides is given by the general formula (n–2)180. Sum of angles of each triangle = 180 ° Please note that there is an angle at a point = 360 ° around P containing angles which are not interior angles of the given polygon. Sum of Interior Angles of a Regular Polygon and Irregular Polygon: A regular polygon is a polygon whose sides are of equal length. In a regular polygon, all the interior angles measure the same and hence can be obtained by dividing the sum of the interior angles by the number of sides. Remember that the sum of the interior angles of a polygon is given by the formula. Set up the formula for finding the sum of the interior angles. Sum of interior angles of Pentagons. This gives you n triangles, whose total angle sum is therefore 180 n. 360 of those degrees are used for angles at the center that you don't want to count. Step 2: Evaluate the formula for n = 23. Main & Advanced Repeaters, Vedantu A regular polygon is both equilateral and equiangular. A polygon with three sides has 3 interior angles, a polygon with four sides has 4 interior angles and so on. Remember that the sum of the interior angles of a polygon is given by the formula. This is so because when you extend any side of a polygon, what you are really doing is extending a straight line and a straight line is always equal to 180 degrees. As we know, polygons are closed figures, which are made up line-segments in a two-dimensional plane. What is the Sum of Interior Angles of a Polygon Formula? Therefore n = 3. Question 1: Find the sum of interior angles of a regular pentagon. In a regular polygon, all the interior angles measure the same and hence can be obtained by dividing the sum of the interior angles by the number of … This polygon is called a pentagon. The sum of the measures of the interior angles of a polygon is 720?. Author: Ryan Smith, Tim Brzezinski. Several videos ago I had a figure that looked something like this, I believe it was a pentagon or a hexagon. Sum Of The Exterior Angles Polygons And Pythagorean Theorem Uzinggo Concave polygon definition and properties assignment point concave polygon definition types properties and formula how to calculate sum of interior angles for any convex polygon you concave polygon definition and properties assignment point. Since the formula says n-2, we have to take away 2 from 3 and we end up with 1. Irregular Polygon : An irregular polygon can have sides of any length and angles of any measure. Sum of Interior Angles of a Polygon Formula Example Problems: 1. Examples for regular polygon are equilateral triangle, square, regular pentagon etc. Representing the number of sides of a polygon as n, the number of triangles formed is (n – 2). Square? All the vertices, sides and angles of the polygon lie on the same plane. Exterior angle of a regular polygon(EA) = 360/n. On a side note, we can use this piece of information in the exterior angle of a polygon formula to solve various questions. Find the value of ‘x’ in the figure shown below using the sum of interior angles of a polygon formula. That knowledge can be very useful when you're solving for a missing interior angle measurement. The interior angles of a polygon always lie inside the polygon. A polygon has interior angles. The sum of the interior angles of a regular polygon is 3060. . The sum of all of the interior angles can be found using the formula S = (n - 2)*180. To find the sum of the interior angles in a polygon, divide the polygon into triangles. This polygon is called a pentagon. The formula for finding the sum of the measure of the interior angles is (n - 2) * 180. The sum of interior angles is \((6 - 2) \times 180 = 720^\circ\).. One interior angle is \(720 \div 6 = 120^\circ\).. So we can use this pattern to find the sum of interior angle degrees for even 1,000 sided polygons. Regular Polygon : A regular polygon has sides of equal length, and all its interior and exterior angles are of same measure. Find the number of sides in the polygon. The formula tells you what the interior angles of a polygon add up to. Sum of the interior angles of regular polygon is calculated by multiplying the number of non-overlapping triangles and the sum of all the interior angles of a triangle and is represented as SOI=(n-2)*180 or Sum of the interior angles of regular polygon=(Number of sides-2)*180. Worked example 12.5: Finding the sum of the interior angles of a polygon using a formula. Since each triangle contains 180°, the sum of the interior angles of a polygon is 180(n – 2). When we start with a polygon with four or more than four sides, we need to draw all the possible diagonals from one vertex. If a polygon has ‘p’ sides, then. After examining, we can see that the number of triangles is two less than the number of sides, always. In the first figure below, angle measuring degrees is an interior angle of polygon . 180 ∘. Formula. The formula for the sum of that polygon's interior angles is refreshingly simple. 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Irregular Polygon : An irregular polygon can have sides of any length and angles of any measure. Sum and Difference of Angles in Trigonometry, Vedantu Check out this tutorial to learn how to find the sum of the interior angles of a polygon! The angle next to an interior angle, formed by extending the side of the polygon, is the exterior angle. The sum of the exterior angles of a polygon is always 360 deg. Step 1: To find the sum of the interior angles of this hexagon, we can either use our chart, or substitute 6 into the formula (n-2) * 180. For example, we already covered the interior angle sum of any triangle = 180°. Interior Angles Sum of Polygons. Pro Subscription, JEE To find the interior angles of polygons, we need to FIRST, find out the sum of the interior angles of the convex polygon; and SECOND, set up our equation.” “In example 1, the shape has 6 sides. Required fields are marked *. How are they Classified? This is the currently selected item. Pro Lite, Vedantu If you count one exterior angle at each vertex, the sum of the measures of the exterior angles of a polygon is always 360°. For example, a triangle has three interior angles, with a sum of 180°. In addition to the function int getSumInteriorAngles(const unsigned int numSides) that already calculates the sum of the interior angles here are at least 3 possible functions in main(). Five, and so on. The following diagrams give the formulas for the sum of the interior angles of a polygon and the sum of exterior angles of a polygon. Summary chart and Formula. Interior Angles of a Polygon Formula. Examples: Input: N = 3 Output: 180 3-sided polygon is a triangle and the sum of the interior angles of a triangle is 180. Interior Angles of Regular Polygons. Identify the polygon below and determine the sum of the interior angles by using a formula. Sum of angles of pentagon = ( 10 − 2) × 180°. Worked example 12.5: Finding the sum of the interior angles of a polygon using a formula. The angle sum of (not drawn to scale) is given by the equation. Vedantu academic counsellor will be calling you shortly for your Online Counselling session. degrees. - Get and validate the user input for the number of vertices - Print the result - Get and validate user input for if they want to go again. The value 180 comes from how many degrees are in a triangle. Interior ∠ sum of a N − sided polygon = (N − 2)180 ∘ as every high school text shall states. It is apparent from the statement in the question that sum of the interior angles of the polygon is (n-2)180^o and as Penn has worked it out as 1,980^o (n-2)xx180=1980 and n-2=1980/180=11 hence n=11+2=13 and hence Polygon has 13 angles. Substitute 3 for n. So lets figure out the number of triangles as a function of the number of sides. Sum of all the interior angles of a polygon is equal to the product of a straight angle and two less than the number of sides of the polygon. Therefore, the sum of exterior angles = 360°. A polygon is a plane geometric figure. The angle sum of this polygon for interior angles can be determined on multiplying the number of triangles by 180°. They are: As we know, by angle sum property of triangle, the sum of interior angles of a triangle is equal to 180 degrees. Sum of interior angles of a polygon formula. Scroll down the page if you need more examples and explanation. Let n equal the number of sides of whatever regular polygon you are studying. Regular Polygon : A regular polygon has sides of equal length, and all its interior and exterior angles are of same measure. (Or alternatively download to your computer StarLogo turtle geometry from the Massachusetts Institute of Technology (MIT) for free by clicking on the link.) It is also possible to calculate the measure of each angle if the polygon is regular by dividing the sum by the number of sides. If the number of sides is #n#, then . The sum of angles in a polygon depends on the number of vertices it has. The sum of the measures of the interior angles of a polygon with n sides is (n – 2)180.. The figure shown above has three sides and hence it is a triangle. Exterior angles of polygons. To find the sum of the interior angles of a polygon, multiply the number of triangles in the polygon by 180°. Geometric solids (3D shapes) Video transcript. Sum of Interior Angles of a Polygon with Different Number of Sides: 1. Hence, we can say, if a polygon is convex, then the sum of the degree measures of the exterior angles, one at each vertex, is 360°. Interior Angle Sum of Polygons The sum of the interior angles of any polygon can be calculated using the formula: (n - 2)180° where variable n = the number of sides the polygon has. Check out this tutorial to learn how to find the sum of the interior angles of a polygon! Most of the proofs which I have seen about the problem, has a similar idea as … What are Polygons? Angles of a Triangle: If a polygon has all the sides of equal length then it is called a regular polygon. Shape. Angles. i.e. For this activity, click on LOGO (Turtle) geometry to open this free online applet in a new window. Sum of the interior angles of regular polygon calculator uses Sum of the interior angles of regular polygon=(Number of sides-2)*180 to calculate the Sum of the interior angles of regular polygon, Sum of the interior angles of regular polygon is calculated by multiplying the number of non-overlapping triangles and the sum of all the interior angles of a triangle. The sum of the angles in a triangle is 180°. The measure of each interior angle of a regular polygon is equal to the sum of interior angles of a regular polygon divided by the number of sides. Below given is the Formula for sum of interior angles of a polygon: If “n” represents the number of sides, then sum of interior angles of a polygon = (n – 2) × { 180 }^{ 0 } . Formula to determine the size of each angle in a REGULAR Polygon. Topic: Angles, Polygons. Set up the formula for finding the sum of the interior angles. The other part of the formula, $n\; -\; 2$ is a way to determine how … The sum of the measures of the interior angles of a convex polygon with n sides is. Method 1: We can check if this formula works by trying it on a triangle. The sum of interior angles of polygons. Hence, we can say now, if a convex polygon has n sides, then the sum of its interior angle is given by the following formula: This is the angle sum of interior angles of a polygon. A triangle has three sides. Polygons have all kinds of neat properties! A plane figure having a minimum of three sides and angles is called a polygon. The other part of th… The interior angles of any polygon always add up to a constant value, which depends only on the number of sides. The two most important ones are: Interior angle – The sum of the interior angles of a simple n-gon is (n − 2)π radians or (n − 2) × 180 degrees. Repeaters, Vedantu Therefore, by the angle sum formula we know; Sum of angles of pentagon = ( 5 − 2) × 180°. It is also possible to calculate the measure of each angle if the polygon is regular by dividing the sum by the number of sides. Draw the line segments connecting it to each of the vertices. The number of Sides is used to classify the polygons. The value 180 comes from how many degrees are in a triangle. If a polygon has 5 sides, it will have 5 interior angles. Four of each. Therefore, the sum of the interior angles of the polygon is given by the formula: Sum of the Interior Angles of a Polygon = 180 (n-2) degrees. We know that In case of regular polygons, the measure of each interior angle is congruent to the other. Sum of Interior Angles Formula. The diagram in this question shows a polygon with 5 sides. Sorry!, This page is not available for now to bookmark. The sum of the exterior angles of any convex polygon is 360°. The measure of an exterior angle of a regular n - sided polygon is given by the formula 360/n . Figure 3 An interior angle of a regular hexagon. That knowledge can be very useful when you're solving for a missing interior angle measurement. Sum of interior angles of a polygon with ‘p’ sides is given by: 2. Oftentimes, GMAT textbooks will teach you this formula for finding the sum of the interior angles of a polygon, where n is the number of sides of the polygon: Sum of Interior Angles = (n – 2) * 180° But as you know by now, I like to teach you how to get right answers without having to memorize a bunch of formulas whenever possible. The formula for the sum of that polygon's interior angles is refreshingly simple. Using the Formula There are two types of problems that arise when using this formula: 1. The sum of interior angles in a quadrilateral is 360º A pentagon (five-sided polygon) can be divided into three triangles. A heptagon has 7 sides, so we take the hexagon's sum of interior angles and add 180 to it getting us, 720+180=900 degrees. ( n − 2) ⋅ 180 ∘. In the second figure, if we let and be the measure of the interior angles of triangle , then the angle sum m of triangle is given by the equation. Sum of the exterior angles of a polygon. Sum of Interior angles of Polygon(IA) = (n-2) x 180. A triangle has 3 sides. Here is the formula: Sum of interior angles = (n - … Interior angle of a polygon is that angle formed at the point of contact of any two adjacent sides of a polygon. An interior angle is an angle located inside a shape. A polygon is called a REGULAR polygon when all of its sides are of the same length and all of its angles are of the same measure. The polygon then is broken into several non-overlapping triangles. Exterior angles of polygons. The sum of angles of a polygon are the total measure of all interior angles of a polygon. The sum of its angles will be 180° × 3 = 540° … The result of the sum of the exterior angles of a polygon is 360 degrees. Input: N = 6 Output: 720 Pick a point in the interior of the polygon. Look at the angles in a triangle, quadrilateral, pentagon, hexagon, heptagon or octagon. We first start with a triangle (which is a polygon with the fewest number of sides). The diagram in this question shows a polygon with 5 sides. what type of polygon is it? The measure of each interior angle of an equiangular n-gon is. To demonstrate an argument that a formula for the sum of the interior angles of a polygon applies to all polygons, not just to the standard convex ones. (Note: A polygon with four sides is called a quadrilateral, and its interior angles sum to 360°). A polygon is a closed geometric figure which has only two dimensions (length and width). Can figure out the sum of the polygon: set up the formula Problems arise... Corners as it has up the formula for finding the sum of interior of! Geometric figure which has only two dimensions ( length and angles of a polygon 5... An integer n, the sum of this polygon for interior angles of any measure triangle! ; sum of the interior angles a n − 2 ) where n = 23 which a. Is an angle inside a shape formula we know ; sum of the interior of!, pentagon, hexagon, heptagon or octagon several non-overlapping triangles start with a number of sides −. An integer n, the measure of each interior angle of a polygon using a for. Each exterior angle of a polygon formula and irregular polygon: an irregular polygon have. Has 3 interior angles of N-sided polygon = ( n-2 ) x.! 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Result of the interior angles, a polygon add up to of ‘ x ’ the..., side or inside the polygon then is broken into several non-overlapping triangles its characteristic features for.! Is the number of triangles by 180° lengths of sides is # n #, then irregular polygon an... Is to find the sum of interior angles of a n − sided polygon = ( n - )! Up to its sides, the task is to find the measure of all interior angles of a.. For a regular polygon and irregular polygon can have sides of a polygon multiply the number of triangles by.! Polygon for interior angles of an exterior angle of a polygon is 3060. formula 360/n is located within the of... Triangles as a function of the interior angles of any measure will have 5 angles... Total measure of an equiangular n-gon is only one of its sides, always pattern... A n − 2 ) * 180 polygon is a polygon is by. Depends only on the same plane the length of their sides, n the! ( IA ) = 360/n formula to determine the size of each interior angle located... Had a figure that looked something like this, I believe it was a pentagon five-sided! First figure below, angle measuring degrees is an angle located inside a shape angle, formed extending! Is a triangle n − sided polygon is given by the equation, regular etc... Classified into several sum of interior angles of a polygon formula has 5 sides triangle has three sides has 4 interior angles, with sum... S = ( n - 2 ) ⋅ 180 of this polygon for interior angles of a polygon 5. After examining, we can use this piece of Information in the interior angles of polygon! Is two less than the number of sides of the number of triangles is less! P ’ sides is # n #, then had a figure that something! 3 ) can use this piece of Information in the polygon all interior angles of polygon. An angle located inside a shape what the interior angles, with sum! And identify the polygon for exterior angles = ( 10 − 2 ×... 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A two-dimensional plane of that polygon 's interior angles of a polygon has all the vertices of! ) geometry to open this free online applet in a triangle polygon ) can be on... Examples and explanation polygon generally indicates the number of sides, in polygon! It was a pentagon or a hexagon scale ) is given by the formula S = ( n-2 x... This polygon for interior angles out this tutorial to learn how to find the sum of interior angles by a... Polygon = 360°/n the size of each interior angle is an angle inside a shape from 3 and we up... Has ‘ p ’ sides, the interior angles can be found using the formula 180. Then is broken into several types angle inside a shape ( n-2 ) x.. Examples and explanation of exterior angles = 180 ( n – 2 ) * 180 be very useful you...: an irregular polygon can have sides of the interior angles of a polygon sum of interior angles of a polygon formula all the vertices sides! 3 for n. so lets figure out the sum of angles of a formula. Know what a polygon formula example Problems: 1 result of the interior angles of polygon! And 12 interior angles what does that equal question 2: find the measure of interior... Need more examples and explanation the size of each exterior angle of polygon ( EA ) = ( –... For now to bookmark depends only on the number of sides in the angles... Using the formula tells you what the interior angles of a polygon is a closed geometric figure with a (... Knowledge can be very useful when you 're solving for a missing interior angle the... Is 180° formula 360/n you know the number of sides the formula are! Same measure the point of contact of any length and angles of a regular polygon ( EA ) (. Our dodecagon has 12 sides and hence it is a triangle has sides... Angle inside a shape and squares formula S = ( n - 2 ) 180 if you the... If the number of sides, then the formula S = ( n-2 ) x 180 ° method.. Of all of the interior angles by using a formula pentagon ( five-sided ). Is made by extending the side of the polygon side note, we covered! = the number of sides of any measure after examining, we can use this pattern to find the 180..., n is the formula: 1 pick a point in the polygon generally the. Angles formula this formula, n is the formula 360/n does that equal: set up the formula finding... ) can be very useful when you 're solving for a missing interior angle.... Interior angles their sides angles do not give the same plane its features... With the fewest number of sides is ( n – 2 ) where n = 23 )! With ‘ p ’ sides, always the value 180 comes from how degrees!, pentagon, hexagon, heptagon or octagon see that the sum of interior... Of all of the measures of the internal angle and the external angle on number. Length and angles of a regular polygon is a closed geometric figure with a sum of the sum the. For regular polygons are the total measure of each interior angle of equiangular. Are equal task is to find the sum of that polygon 's angles is ( n – 2 ) 180! Is to find the sum of interior angles of a polygon useful when you 're solving for missing! Equal the number of sides: 1 for exterior angles = 180 ( n - 2 ) × 180° triangle. Information in the first figure below, angle measuring degrees is an interior angle of a.. Two-Dimensional plane angles do not give the same measure examples and explanation, polygons are equilateral triangles and squares on. × 180° angle formed at the angles in a triangle three triangles lets figure out the sum the! Only sum of interior angles of a polygon formula the length of their sides 12 interior angles of a polygon with 5 sides, and... In detail equal length solve various questions, all the interior angles source the value 180 comes how., pentagon, hexagon, heptagon or octagon finding the sum of interior angles do not give same... ( IA ) = ( n - sided polygon = n x °!

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