Question

The number of sides of a regular polygon where each exterior angle has a measure of $45°$:

• A. $8$
• B. $10$
• C. $4$
• D. $6$

Answer 1

The correct option is A

$8$

Explanation for correct option:

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$=45°$

$\therefore 45=\frac{360}{\mathrm{n}}$

$\mathrm{n}=\frac{360}{45}$

$\mathrm{n}=8$

Therefore, the number of sides in this polygon is '$8$'

Hence, option(A) is the correct answer.