# High School Math : Pentagons

## Example Questions

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### 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 #491 : Plane Geometry

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

Explanation:

The measure of an interior angle of a regular polygon can be determined using the following equation, where  equals the number of sides:

### Example Question #1 : Pentagons

What is the perimeter of the pentagon?

Explanation:

The perimeter of a polygon is found by calculating the sum of all of the side lengths. In this instance, the polygon is regular, so the perimeter can be found by mulitplying the length of one side by the total number of sides:

### Example Question #1 : Pentagons

Find the length of the diagonal of the following pentagon:

Explanation:

Use the Pythagorean Theorem to find the length of the diagonal:

### Example Question #7 : Pentagons

Find the length of the diagonal of the following pentagon:

Explanation:

Use the Pythagorean Theorem to find the length of the diagonal:

### Example Question #8 : Pentagons

What is the side length of a regular pentagon with a perimeter of ?

Explanation:

To find the side length of a regular pentagon with a perimeter of  you must use the equation for the perimeter of a pentagon.

The equation is

Plug in the numbers for perimeter and number of sides to get

Divide each side of the equation by the number of sides to get the answer for the side length.

The answer is .

### Example Question #1 : Pentagons

Find the length of the side of the following pentagon.

The perimeter of the pentagon is .

Explanation:

The formula for the perimeter of a regular pentagon is

,

where  represents the length of the side.

Plugging in our values, we get:

### Example Question #10 : Pentagons

Find the length of the side of the following pentagon.

The perimeter of the pentagon is .

Explanation:

The formula for the perimeter of a regular pentagon is

,

where  represents the length of the side.

Plugging in our values, we get:

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