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

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

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

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

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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. A B. 360

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

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

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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

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Example 7: Find the value of x

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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

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Example 9:

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Wrap-up: 1. How do you find the sum of the interior angles in a polygon? 2. How do you find the sum of the exterior angles in a polygon? 3. Why do you need to know this?

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Todays Work

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