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Published byCory Chambers Modified over 6 years ago

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8.1.1 Find Angle Measures in Quadrilaterals Chapter 8: Quadrilaterals

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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

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

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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

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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

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

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