Determine the Size of Angles in Polygons

Polygons

Interior & Exterior Angles of Polygons

​Dr. Tom Giles

What is a Polygon?

​A closed figure bounded by straight lines

A Regular Polygon has All Equal Angles

The Sum of all Interior Angles of Polygon can be calculated by determining the number of triangles in the Polygon and multiplying that number by 180 degrees

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

Fill in the Blanks

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

Fill in the Blanks

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

Fill in the Blanks

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

Answer: 10 sides

Fill in the Blanks

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.