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.

Answer

108 degrees

Steps to Solve

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 $.

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 $.

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

More Information

In a regular pentagon, not only are all interior angles equal, but all sides are also of equal length. Regular polygons have many symmetrical properties that are interesting in the study of geometry.

Tips

A common mistake is forgetting to use the correct formula for the sum of the interior angles of a polygon, or failing to remember to divide by the number of sides to get the measure of each interior angle.

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