 ## Presentation on theme: "8.1.1 Find Angle Measures in Quadrilaterals Chapter 8: Quadrilaterals."— Presentation transcript:

Polygon Interior Angles Theorem Question: What happens when you add triangles (3 sides)? Answer: first, quadrilaterals (4 sides, “2 triangles”) Second, pentagons (5 sides, “3 triangles”) Hexagons (6 sides, “4 triangles”) Heptagon (7 sides, “5 triangles”) Octagons (8 sides, “6 triangles”) Nonagons (9 sides, “7 triangles”) Decagons (10 sides, “8 triangles”) Dodecagon (12 sides, “10 triangles”) Decemyriagon (100,000 sides, “99,998 triangles”) N-gon (n sides, “n-2 triangles”) For any polygon with n sides the sum of the interior angles is (n – 2)*180

Example: Quadrilateral 180 ⁰ + = 360 ⁰ Check: (n – 2) * 180 = 4 -2 * 180 = 2 * 180 = 360

Polygon Exterior Angles Theorem For any polygon, the sum of the exterior angles is 360 ⁰ m  1 + m  2 + m  3 + m  4 + m  5 = 360⁰ 1 2 3 4 5

Find the Value of x 155 ⁰ (x +75)⁰ 155 ⁰ 166 ⁰ 160⁰ 175 ⁰ (x + 10)⁰ 85⁰ 125⁰ 155⁰ 170⁰ 165⁰

Homework p. 510 2, 3 – 15odd, 18, 22, 24, 25, 28, 29