How many degrees is a regular pentagon?

Understand the Problem

The question is asking for the measure of each interior angle of a regular pentagon, which is a five-sided polygon. To find this, we need to use the formula for calculating the interior angles of a polygon.

108 degrees

The measure of each interior angle of a regular pentagon is 108 degrees

Steps to Solve

1. Identify the formula for the sum of interior angles of a polygon

The formula for the sum of the interior angles of a polygon with $n$ sides is $(n-2) imes 180^\circ$.

1. Calculate the sum of the interior angles for a pentagon

Substitute $n = 5$ into the formula:

$$(5-2) imes 180^\circ = 3 imes 180^\circ$$

Therefore, the sum of the interior angles of a pentagon is $540^\circ$.

1. Calculate the measure of each interior angle in a regular pentagon

Since all interior angles in a regular pentagon are equal, divide the sum of the interior angles by 5:

$$\frac{540^\circ}{5} = 108^\circ$$

The measure of each interior angle of a regular pentagon is 108 degrees