Interior & Exterior Angles of Polygons

Polygons

Interior and Exterior Angles

Dr. Tom Giles

Interior and Exterior Angles

Sum of Interior Angles for Regular Polygon = (n-2) 180

Sum of Exterior Angles for Any Polygon = 360

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For a regular NONAGON, find the measure of one interior angle.

$\degree$  

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For a regular 15-gon, find the measure of one interior angle.

$\degree$  

Interior Angle Sum

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If the sum of interior angles of a polygon is  $900\degree$  , how many sides does the polygon have?

Answer: 7 sides

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If the sum of the interior angles of a polygon is $2880\degree$ , how many sides does the polygon have? 

Exterior Angles

Multiple Choice

Select the correct values for a and m.

• a=50, m=89

• a=50, m=116

• a=105, m=89

• a=105, m=116

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What is the value of each exterior angle of a regular 20-gon?

$\degree$   

Measure of Each Exterior Angle (for regular polygons)

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The measure of an exterior angle of a regular polygon is $45\degree$  .

Find the number of sides of the polygon. 

Answer: 8 sides

Interior and Exterior Angles

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Practice: The measure of an interior angle of a regular polygon is  $144\degree$  . How many sides does the polygon have?

Answer: 10 sides

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Practice:  If the measure of one interior angle of a regular polygon is $160\degree$  , find the number of sides. 

Open Ended

Is it possible for a regular polygon to have an interior angle measure of

$$158\degree$$  ? Explain why or why not. 

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