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Chapter 8.1 Notes: Find Angle Measures in Polygons Goal: You will find interior and exterior angle measures in polygons.

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Properties of a Polygon In a polygon, two vertices that are endpoints of the same side are called consecutive vertices. A diagonal of a polygon is a segment that joins two nonconsecutive vertices.

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Finding Interior Angle Measures in Polygons Theorem 8.1 Polygon Interior Angles Theorem: The sum of the measures of the interior angles of a convex n-gon is (n – 2)180.

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Corollary to Theorem 8.1 Interior Angles of a Quadrilateral: The sum of the measures of the interior angles of a quadrilateral is 360 o. Ex.1: Find the sum of the measures of the interior angles of a convex octagon.

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GUIDED PRACTICE for Examples 1 and 2 The coin shown is in the shape of a regular 11- gon. Find the sum of the measures of the interior angles. 1. ANSWER 1620° The sum of the measures of the interior angles of a convex polygon is 1440°. Classify the polygon by the number of sides. 2. ANSWER decagon

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Ex.2: The sum of the measures of the interior angles of a convex polygon is 900 o. Classify the polygon by the number of sides. Ex.3: Find the value of x in the diagram shown.

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Ex.4: In the diagram below, find and Ex.5: The sum of the measures of the interior angles of a convex polygon is 1440 o. Classify the polygon by the number of sides.

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Finding Exterior Angle Measures in Polygons 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 o.

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Exterior Angle Sum Theorem Exterior Angle Sum Theorem If a polygon is convex, then the sum of the measures of the exterior angles, one at each vertex, is 360°.

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Ex.6: What is the value of x in the diagram shown? Ex.7: A convex hexagon has exterior angles with measures 34 o, 49 o, 58 o, 67 o, and 75 o. What is the measure of an exterior angle at the sixth vertex?

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Ex.8: The trampoline shown is shaped like a regular dodecagon. Find (a) the measure of each interior angle, and (b) the measure of each exterior angle. Ex.9: A stop sign is shaped like a regular octagon. Find (a) the measure of each interior angle, and (b ) the measure of each exterior angle.

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