# Interior Angles in a Regular Polygon

- Author:
- justin.brennan, Irina Boyadzhiev

- Topic:
- Angles

What is the relationship (and ultimately the equation) between the number of sides of a regular polygon and the interior angle measure.

1) First determine the relationship between the number of sides of a regular polygon,

**and the number of triangles that can be made. 2) Considering the triangle angle sum theorem tells us that the sum of all interior angles of a triangle are 180 degrees, what can we say about the sum of all of the interior angles in a regular polygon? 3) In a regular polygon, all interior angles are the same measurement. Knowing this, how can we find the measure of a specific interior angle of a regular polygon? 4) What is the interior angle measure of an octogon? 5) The interior angle of a regular polygon is 157.5 degrees. How many sides does it have?***n*