# High School Math : How to find an angle in a pentagon

## Example Questions

### Example Question #1 : Pentagons

What is the interior angle measure of any regular pentagon?

Explanation:

To find the angle of any regular polygon you find the number of sides . For a pentagon, .

You then subtract 2 from the number of sides yielding 3.

Take 3 and multiply it by 180 degrees to yield the total number of degrees in the regular pentagon.

Then to find one individual angle we divide 540 by the total number of angles 5,

The answer is .

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

What is the measure of each interior angle of a regular pentagon?

Explanation:

The following equation can be used to determine the measure of an interior angle of a regular polygon, where  equals the number of sides.

In a pentagon, .

Now we can solve for the angle.

### Example Question #3 : Pentagons

Find the interior angle of the following regular pentagon:

Explanation:

The formula for the sum of the interior angles of a polygon is

,

where  is the number of sides in the polygon

Plugging in our values, we get:

Dividing the sum of the interior angles by the number of angles in the polygon, we get the value for each interior angle:

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

What is the measure of an interior angle of a regular pentagon?