Interior Angles in Regular Polygons

Concept

The angles that lie inside a shape, generally a polygon, are said to be interior angles.

Rules

1. To find the measure of one interior angle in a regular polygon, first find the sum of interior angles of the required polygon using the formula given below.

Sum of interior angles = (n – 2) ∙ 180°

2. Next, divide the sum of interior angles by the total number of angles the regular polygon has.

$\fn_phv \frac{(n-2)\times 180^{\circ}}{n}$

Example

What is the measure of each interior angle in a regular decagon?

Solution

To find the measure of one interior angle in a regular polygon, first find the sum of interior angles of the required polygon using the formula given below.

Sum of interior angles = (n – 2) ∙ 180°

A decagon has 10 sides, so:
(10 – 2) ∙ 180 = 8 ∙ 180° = 1,440°

Since this is a regular decagon, all of the angles are equal, so divide the sum of the interior angles by 10.

$\fn_phv \frac{1,440^{\circ}}{10}={\color{Red} 144^{\circ}}$