Lesson 3.5 AIM: The Polygon Exterior Angle Sum Theorem

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Find Angle Measures in Polygons

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Presentation transcript:

Lesson 3.5 AIM: The Polygon Exterior Angle Sum Theorem Do Now: Find the measure of Angle A. Step 1: How many sides in the shape? 5 sides Step 2: Sum of Interior Angles? (n - 2)180 (5 - 2)180 = 540º Step 3: Subtract Given Angles. 540 - 113 - 80 - 130 - 90 = 127º

The sum of the measures of the exterior angles in a polygon is 360º

The sum of an exterior and interior angle is 180º

Find the value of x. The sum of exterior angles = 360º x + 2x + 85 + 95 = 360 3x + 180 = 360 - 180 -180 3x = 180 3 3 x = 60º

Find the number of sides of the regular polygon with the exterior angle measure of 60º. a. What is the measure of one of the interior angles? 180 - 60 = 120º Use the polygon exterior angle theorem to find the number of sides. 360º ÷ 60º = 6 sides

Summary Question