Angle Sums of Polygon

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

Interior Angle Sum

Answer: 7 sides

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

Measure of Each Exterior Angle (for regular polygons)

Answer: 8 sides

Interior and Exterior Angles

Answer: 10 sides

Open Ended

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

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