10-2: Diagonals and Angle Measure

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Presentation transcript:

10-2: Diagonals and Angle Measure

10-2: Diagonals and Angle Measure Theorem 10-1: If a convex polygon has n sides, then the sum of the measures of its interior angles is (n – 2)180. 180˚ 180˚ 180˚ 180˚ 180˚

10-2: Diagonals and Angle Measure Example Landscapers often need to know interior angle measures of polygons in order to correctly cut wooden borders for garden beds. The border at the right is a regular hexagon. Find the sum of measures of its interior angles. (6 – 2)(180) = 720˚ Find the measure of one interior angle of the hexagon. 720 / 6 = 120˚

10-2: Diagonals and Angle Measure YOUR TURN Refer to the figure at the right. Find the sum of measures of the interior angles. 1080˚ Find the measure of one interior angle 135˚

10-2: Diagonals and Angle Measure Theorem 10-2: In any convex polygon, the sum of the measures of the exterior angles, one at each vertex, is 360. Proof n linear pairs – sum of interior angles 180n – 180(n – 2) 180n – 180n + 360 360

10-2: Diagonals and Angle Measure Find the measure of one exterior angle of a regular heptagon Heptagon = 7 sides 360 / 7  51˚ YOUR TURN Find the measure of one exterior angle of a regular quadrilateral. 90˚

10-2: Diagonals and Angle Measure Assignment Worksheet #10-2