Question

One angle of a regular polygon is 144°. How many sides does it have?

Answer 1

Measure of one angle of a regular polygon = 144°

We know that the measure of each angle of a regular polygon is equal.

∴ Measure of each angle of the regular polygon = 144°

Let the number of sides of the given regular polygon be n.

We know that the sum of the angles of a polygon with n sides = (n −2) × 180°

⇒ 144° × n = (n − 2) × 180°

Thus, the given regular polygon has 10 sides.