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Published byMelanie Fletcher Modified over 9 years ago
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Section 8 – 1 Find Angle Measures in Polygons
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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◦.
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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◦.
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Classifying Polygons Number of Sides Type of Polygon Number of Sides Type of Polygon 3Triangle8Octagon 4 Quadrilateral 9Nonagon 5Pentagon10Decagon 6Hexagon12Dodecagon 7Heptagonnn-gon
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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◦
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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◦ = 2340 180◦ 180◦ n – 2 = 13 n = 15 -gon
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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
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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◦
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Homework Section 8-1 Page 510 – 513 3 – 10, 11 – 15, 19, 20, 30, 39 – 41, 44 - 47
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