### All PSAT Math Resources

## Example Questions

### Example Question #1 : How To Find An Angle In A Pentagon

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

**Possible Answers:**

144

120

108

72

180

**Correct answer:**

108

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 #1 : How To Find An Angle In A Pentagon

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

Evaluate .

**Possible Answers:**

**Correct answer:**

By angle addition,

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,

Certified Tutor

Certified Tutor