Question

Find the number of sides in a regular polygon, if its each exterior angle is $\frac{1}{3}$ of a right angle

• A. $12$
• B. $19$
• C. $11$
• D. $15$

Answer 1

The correct option is A $12$

Sum of all exterior angles of a polygon is ${360}^o$
Given that each exterior angle is one third of a right angle.
Let number of side = $n$ (which is must be an integer)
$n\times \frac{1}{3}\times {90}^o={360}^o$
$n=12$