Statement: In a polygon of ‘n’ sides, the sum of the interior angles is equal to (2n – 4) × 90°. What if we needed to find the interior angle of a regular polygon with 100 sides? (1) 8 sides (2) 9 sides (3) 12 sides (4) 6 sides Answer by rothauserc(4717) (Show Source): That might be a little difficult to draw! In order to find the measure of a single interior angle of a regular polygon (a polygon with sides of equal length and angles of equal measure) with n sides, we calculate the sum interior anglesor $$ (\red n-2) \cdot 180 $$ and then divide that sum by the number of sides or $$ \red n$$. The polygon in Figure 1 has seven sides, so using Theorem 39 gives: . An exterior angle of a polygon is formed by extending only one of its sides. The point P chosen may not be on the vertex, side or inside the polygon. Polygons Interior Angles Theorem. The number of triangles is always two less than the number of sides. Examples: Input: N = 3 Output: 180 3-sided polygon is a triangle and the sum of the interior angles … Figure 1 Triangulation of a seven‐sided polygon to find the interior angle sum.. Theorem 39: If a convex polygon has n sides, then its interior angle sum is given by the following equation: S = ( n −2) × 180°. Given an integer N, the task is to find the sum of interior angles of an N-sided polygon. Students also learn the following formulas related to convex polygons. The following diagram shows the formula for the sum of interior angles of an n-sided polygon and the size of an interior angle of a n-sided regular polygon. Sum of interior angles of n-sided polygon = n x 180 ° - 360 ° = (n-2) x 180 ° Method 4 . How many sides does the polygon have? Here are two methods to find the measure of the interior angles of a regular polygon: For both methods, we will use the fact that the sum of the measures of the interior angles of a … 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. The sum of the interior angles of a polygon is 180 (n – 2), where n represents the number of sides. Count the number of sides in each of the polygons featured in this batch of worksheets for 6th grade and 7th grade students. This gives us the formula The regular polygon with the fewest sides -- three -- is the equilateral triangle. The formula is = (−) ×, where is the sum of the interior angles of the polygon, and equals the number of sides in the polygon.. Scroll down the page for more examples and solutions on the interior angles of a polygon. Set up the formula for finding the sum of the interior angles. Regular polygons exist without limit (theoretically), but as you get more and more sides, the polygon looks more and more like a circle. Add the interior angles, set the sum equal to 720, and solve for x: About the Book Author. The other part of the formula, − is a way to determine how many triangles the polygon can be divided into. A polygon with 23 sides has a total of 3780 degrees. Example: Find the sum of the interior angles of a heptagon (7-sided) Solution: Below is the proof for the polygon interior angle sum theorem. The sum of the angles of a hexagon (six sides) is equal to . Interior Angle = Sum of the interior angles of a polygon / n. Where “n” is the number of polygon 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°. Sum of Interior Angles of a Polygon. 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