Question

The number of sides of a regular polygon, if each of its interior angles is ${135}^{\circ }$, is given by

• A. 4
• B. 6
• C. 8
• D. 10

Answer 1

The correct option is C 8

Formula for sum S of n interior angles of n sided polygon is
$S=(n-2)\times \mathring{180}$
Since polygon is regular all its interior angles is same, sum of them is 135 degree times n
So we have S=$\mathring{135n}$
As per formula,
$S=(n-2)\times \mathring{180=\stackrel{˚}{135n}}$
$180(n-2)=135n$
$180n-360=135n$
$45n=360$
$n=\frac{360}{45}=8$
Number of sides is 8