Section 8 – 1 Find Angle Measures in Polygons

Theorem 8.1 Polygon Interior Angles Theorem: The sum of the measures of the angles of a convex n-gon is (n – 2) 180◦. n = number of sides Corollary to Theorem 8.1 Interior Angles of a Quadrilateral: The sum of the measures of the interior angles of a quadrilateral is 360◦.

Theorem 8.2 Polygon Exterior Angles Theorem: The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is 360◦.

Classifying Polygons Number of Sides Type of Polygon Number of Sides Type of Polygon 3Triangle8Octagon 4 Quadrilateral 9Nonagon 5Pentagon10Decagon 6Hexagon12Dodecagon 7Heptagonnn-gon

Example 1 Find the sum of the measures of the interior angles of a convex nonagon. How many sides does a nonagon have: 9 Use the Polygon Interior Angles Theorem: (n – 2) 180◦ (9 – 2) 180◦ (7) 180◦ 1260◦

Example 2 The sum of the measures of the interior angles of a convex polygon is 2340◦. Classify the polygon by the number of sides. Use the Polygon Interior Angles Theorem: (n – 2) 180◦ (n – 2) 180◦ = ◦ 180◦ n – 2 = 13 n = 15 -gon

Example 3 Find the value of x in the diagram shown. Use the Polygon Interior Angles Theorem: x◦ + 121◦ + 96◦ + 101◦ + 162◦ + 90° = 720◦ x + 570◦ = 720◦ x = 150◦ (6 – 2) 180◦ =720

Example 4 Find the value of x in the diagram shown. Use the Polygon Exterior Angles Theorem: x◦ + 77◦ + 2x◦ + 45◦ + 40° = 360◦ 3x + 162◦ = 360◦ 3x = 198◦ x = 66◦

Homework Section 8-1 Page 510 – – 10, 11 – 15, 19, 20, 30, 39 – 41,