Question

If each interior angle of a regular polygon is 135°, then the number of sides that polygon has is:

• A. 10
• B. 12
• C. 15
• D. 8

Answer 1

Answer:

D. 8

Solution:

Given :

The interior angle of a polygon is 135^o.

Formula used:

Sum of interior angle = (n - 2) × 180^o [Where n is the number of sides of the polygon]

Calculation:

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

So it can be written,

135° × n = (n - 2) × 180°

⇒ 135° × n = n × 180° - 360°

⇒ 45° × n = 360°

=>n =\frac{306^o}{45^o}=8

Hence, the number of sides of the polygon is 8.