Question

Find the number of sides of a regular polygon if each interior angle of the polygon is 108°​

Answer 1

Answer: 5

Step-by-step explanation: Each interior angle of the polygon is 108 degrees, so each exterior angle of the polygon is 180-108 = 72 degrees. So the number of sides is 360/72 = 5.

Answer 2

Given :

• Each interior angle of a regular polygon = 108°

To find.

• The number of sides of the regular polygon

Solution :

A polygon whose all sides, interior and exterior angles are equal to each other is known as a regular polygon.

Firstly, we will calculate the exterior angle of the polygon :-

Using formula,

• Interior angle + Exterior angle = 180°

Substituting the given values :-

→ 108° + Exterior angle = 180°

→ Exterior angle = 180° - 108°

→ Exterior angle = 72°

Now, to calculate the number of sides of the regular polygon we will use the following formula :-

• Exterior angle = 360°/n

where,

• n denotes the number of sides of the polygon

Substituting the given values :-

→ 72° = 360°/n

→ n = 360°/72°

→ n = 180°/36°

→ n = 90°/18°

→ n = 5

Therefore, the number of sides of the regular polygon = 5