Question

The number of sides of a regular polygon, where each exterior angle has a measure of '$36°$', is_

Answer 1

Finding the number of sides in the regular polygon:

$\Rightarrow$ The sum of all the exterior angles of a regular polygon, having $\mathrm{n}$ sides$=360°$

$\Rightarrow$The measure of each exterior angle of a regular polygon$=\frac{360°}{\mathrm{n}}$

$\Rightarrow$Here, the measure of each exterior angle$=36°$

$\therefore 36=\frac{360}{\mathrm{n}}$

$\mathrm{n}=\frac{360}{36}$

$\mathrm{n}=10$

Therefore, the number of sides in this polygon is '$10$'.