Working with Angles in a Polygon

By S. Mahandru, Mathematics Subject Lead at Exam.tips

A polygon refers to a shape with multiple sides, which are straight, such as a pentagon, hexagon, or octagon.

You can determine the sum of the interior angles of a polygon by means of this formula:

S = (n - 2)\times 180^\circ

where n represents the number of sides.

Example:

A regular polygon has 5 sides.

The sum of interior angles may be calculated as:

(5-2)\times180^\circ=540^\circ

Each regular polygon has equal angles.

Therefore, each angle = total ÷ number of sides.

For a regular pentagon:

\text{Each interior angle}= \frac{S}{5}= \frac{540^\circ}{5}= 108^\circ.

Angles occur in polygons, architecture, engineering, and artwork.

They will help you understand how to design with accuracy.