Question

Find the number of sides of a regular polygon whose each exterior angle has a measure of 45°​

Answer 1

Given :

• A regular polygon whose each exterior angle has a measure of 45 degrees

To Find :

• The number of sides of a regular polygon?

Solution :

A regular polygon whose each exterior angle has a measure of 45 degrees

Let n be the no. of sides

So, $\sf{\dfrac{360}{n} = 45}$

$\sf{ n = \dfrac{360}{45}}$

$\large{\underline{\underline{\bold{\pink{ n = 8}}}}}$

Answer 2

Sum of the exterior angles of regular polygon

$\huge \bold \red{ = {360}^{∘} }$

But each exterior angle

$\huge \bold{ \color{navy}{ = {45}^{∘} }}$

Number of sides of regular polygon

$\huge \bold \purple{ \frac{ {360}^{∘} }{ {45}^{∘} } = 8 }$

$\huge \mathcal \colorbox{black}{ \blue{@Janvi}}$