# Concept: Angle Measures in Polygons

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Concept: Angle Measures in Polygons
Date: Sec 8-1 Concept: Angle Measures in Polygons Objective: Given a polygon, determine the measures of angles as measured by a s.g.

Sum of the measures of the interior angles in a polygon
Sum of interior angles = (n-2)180, Where n = number of sides

Example 1: Find the value of x
= 456 =84 S= (n-2)180 S=(5-2)180 S=540

Example 2: Find the value of x
S= (n-2)180 S=(8-2)180 S=(6)180 S=1080 X= 1080/8 X = 135 X

Example 3: The sum of the measures of the interior angles in a convex polygon is given. Classify the polygon by the number of sides. B. 360 A

Example 4: Find the measure of each angle in a regular 11-gon
(11-2)180 11 Each angle = 147.3

Example 5: The measure of each interior angle of a regular polygon is How many sides does the polygon have? (n-2)180 = 165 n Cross mult. (n-2)180 = 165n 180n-360 = 165n -180n n -360 = -15n 24 = n

Sum of the exterior angles in a polygon is always 360
Example 6: What is the measure of each exterior angle in a regular hexagon? =360/6 =60

Example 7: Find the value of x

Example 8: The measure of each exterior angle of a regular polygon is 40. How many sides does the polygon have? 360/40 =9 sides

Example 9:

Wrap-up: How do you find the sum of the interior angles in a polygon?
How do you find the sum of the exterior angles in a polygon? Why do you need to know this?

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