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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.

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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**

= 456 =84 S= (n-2)180 S=(5-2)180 S=540

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**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

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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. B. 360 A

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**Example 4: Find the measure of each angle in a regular 11-gon**

(11-2)180 11 Each angle = 147.3

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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

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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: 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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1.What is the measure of 1 interior angle of a regular octagon? 2. How many sides does a regular polygon have with the measure of 1 interior angle of 156⁰?

1.What is the measure of 1 interior angle of a regular octagon? 2. How many sides does a regular polygon have with the measure of 1 interior angle of 156⁰?

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