Calculate the interior angle of a 5 - sided regular polygon

Answer Details

A regular polygon is a polygon where all sides and all interior angles are equal. To find the measure of each interior angle of a regular polygon, you first need to understand the formula for the sum of the interior angles of any polygon.

The sum of the interior angles of an n-sided polygon is:

\[ \text{Sum of interior angles} = (n - 2) \times 180^\circ \]

For a regular polygon, every angle is equal, so you can find the measure of each interior angle by dividing the sum by the number of sides:

\[ \text{Each interior angle} = \frac{\text{Sum of interior angles}}{n} \]

For a 5-sided regular polygon (also called a pentagon):

• \( n = 5 \)

\[ \text{Sum of interior angles} = (5-2)\times180^\circ = 3\times180^\circ = 540^\circ \]

Each angle:

\[ \text{Each interior angle} = \frac{540^\circ}{5} = 108^\circ \]

So, the interior angle of a regular pentagon (5-sided regular polygon) is 108º. This is because the total degrees in all interior angles must split equally among the 5 corners, and using the formula for regular polygons leads directly to this answer.