Question

Find the number of sides in a regular polygon, if its each exterior angle is two-fifth of a right angle.

• A. $10$
• B. $8$
• C. $6$
• D. $5$

Answer 1

The correct option is A $10$

Polygon whose each exterior angle is two-fifth of a right angle $=$ $\frac{2}{5}\times {90}^o={36}^o$.
Sum of all exterior angle of any polygon is ${360}^o$.
$\therefore {36}^o\times \text{number of angles}={360}^o$
$\text{number of angles}=10$
Any polygon have equal number of angles and sides.
Therefore, number of side of polygon is $10$.