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

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

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.

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.

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.

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

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.

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.

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.

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°.

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?

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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