Question

How many sides does a regular polygon have, if measure of each of its interior angle is ${160}^o$?

• A. $18$
• B. $16$
• C. $15$
• D. $20$

Answer 1

The correct option is A $18$

Let the number of sides of the polygon be $n$

Sum of the interior angles of a polygon of $n$ sides is ${180}^0(n-2)$ ...(1)

As the polygon is a regular polygon, each of its angle will be equal $={160}^o$.
This means, sum of all its interior angles $=n\times {160}^o$. ...(2)
From eqn $\left(1\right)$ and $\left(2\right)$, we get
$n\times {160}^o={180}^0(n-2)$
$=>n\times 8=9(n-2)$
$=>8n=9n-18$
$=>n=18$