8.1.1 Find Angle Measures in Quadrilaterals

Chapter 8: Quadrilaterals

Polygon Interior Angles TheoremQuestion:

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 sidesthe sum of the interior angles is (n – 2)*180

Example: Quadrilateral

180 ⁰

+

180 ⁰

= 360⁰

Check:(n – 2) * 180 =4 -2 * 180 = 2 * 180 =360

Polygon Exterior Angles TheoremFor any polygon, the sum of the exterior angles

is 360⁰m1 + m2 + m3 + m4 + m5 = 360⁰

12

3

4

5

Find the Value of x

155⁰(x +75)⁰

155⁰

166⁰

160⁰

175⁰

(x + 10)⁰85⁰

125⁰

155⁰

170⁰

165⁰

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