# PSAT Math : Pentagons

## Example Questions

### Example Question #1 : Pentagons

What is the measure, in degrees, of one interior angle of a regular pentagon?

108

180

72

120

144

108

Explanation:

The formula for the sum of the interior angles of any regular polygon is as follows:

where  is equal to the number of sides of the regular polygon.

Therefore, the sum of the interior angles for a regular pentagon is:

To find the measure of one interior angle of a regular pentagon, simply divide by the number of sides (or number of interior angles):

The measure of one interior angle of a regular pentagon is 108 degrees.

### Example Question #2 : Pentagons

Refer to the above figure, which shows Square   and regular Pentagon .

Evaluate .

Explanation:

is one of two acute angles of isosceles right triangle , so .

To find  we examine .

is an angle of a regular pentagon and has measure .

Also, since, in , sides , by the Isosceles Triangle Theorem,

Since the angles of a triangle must total  in measure,