The value 180 comes from how many degrees are in a triangle. A polygon with 23 sides has a total of 3780 degrees. 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. 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 $$ \red n$$. To prove: Count the number of sides in each of the polygons featured in this batch of worksheets for 6th grade and 7th grade students. An exterior angle of a polygon is formed by extending only one of its sides. Interior Angle of a Regular Polygon | Easy. 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 angles of a hexagon (six sides) is equal to . The sum of the interior angles of a polygon is 180 (n – 2), where n represents the number of sides. A plane figure having a minimum of three sides and angles is called a polygon. The other part of the formula, − is a way to determine how many triangles the polygon can be divided into. Example: Find the sum of the interior angles of a heptagon (7-sided) Solution: (1) 8 sides (2) 9 sides (3) 12 sides (4) 6 sides Answer by rothauserc(4717) (Show Source): 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°. Scroll down the page for more examples and solutions on the interior angles of a polygon. Regular polygons exist without limit (theoretically), but as you get more and more sides, the polygon looks more and more like a circle. Divide the given sum of the interior angles by the number of angles in the polygon to find the size of each interior angle. Below is the proof for the polygon interior angle sum theorem. The number of triangles is always two less than the number of sides. 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? Given an integer N, the task is to find the sum of interior angles of an N-sided polygon. What if we needed to find the interior angle of a regular polygon with 100 sides? The formula is = (−) ×, where is the sum of the interior angles of the polygon, and equals the number of sides in the polygon.. Students also learn the following formulas related to convex polygons. Question 1057870: The sum of the interior angles of a polygon is twice the sum of its exterior angles. 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 … This gives us the formula The sum of the measures of the interior angles of a polygon is always 180(n-2) degrees, where n represents the number of sides of the polygon. 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°. Add the interior angles, set the sum equal to 720, and solve for x: About the Book Author. Polygons Interior Angles Theorem. Students learn the definitions of vertices and diagonals of polygons. Interior Angle = Sum of the interior angles of a polygon / n. Where “n” is the number of polygon sides. Set up the formula for finding the sum of the interior angles. 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