Question

If each exterior angle of a regular polygon is ${36}^{\circ }$, then find the number of sides of the polygon and hence name the polygon.

• A. 9 sides, Nonagon
• B. 7 sides, Heptagon
• C. 5 sides, Pentagon
• D. 10 sides, Decagon

Answer 1

The correct option is D 10 sides, Decagon

Given: Measure of each exterior angle = ${36}^{\circ }$
We know that, sum of all the exterior angles = ${360}^o$

$\therefore$ Number of sides $\times$ each exterior angle = ${360}^{\circ }$
Number of sides = $\frac{{360}^{\circ }}{{36}^{\circ }}$ = 10 sides
10 sided polygon is called a decagon.