Chapter 8.1 Notes: Find Angle Measures in Polygons Goal: You will find 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

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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.

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.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

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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 o .

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.