Lesson 7.1 Interior and Exterior Angles Learning Goal: I can prove the following theorems about triangles: The measures of interior angles of a triangle sum to 180. (Standard G-CO.C.10) EXPLORE Exploring Interior Angles in Polygons Read and complete the following (adapted from Lesson 7.1). Show all your work. interior angles LAL Math Resources http://Bit.ly/L4LMath An interior angle is an angle formed by two sides of a polygon with a common vertex. When we rearrange the interior angles of a triangle, we find that they form a straight angle, measuring 180. The Triangle-Angle Sum Theorem The sum of the angle measures of a triangle is 180. To determine the sum of the interior angles for any polygon, you can consider how many triangles there are in other polygons. If a convex polygon is broken up into triangles, then the sum of the interior angles is the number of triangles times 180. For example, by drawing the diagonal from a vertex of a quadrilateral, you can form two triangles. Since each triangle has an angle sum of 180, the quadrilateral must have an angle sum of 2(180) = 360 In each of the figures below, how many triangles do you see? Triangle Triangle(s) Quadrilateral Triangle(s) Pentagon Triangle(s) Hexagon Heptagon Octagon Triangle(s) _Triangle(s) Triangle(s) For each polygon, identify the number of sides, the number of triangles and determine the angle sums of those triangles. Remember that the sum of the angle measures of a triangle is 180. Polygon Triangle Number of Sides 3 Quadrilateral 4 Pentagon Number of Triangles 1 2 bond Sum of Interior Angle Measures x 180 = x 180 = x 180 = x 180 =