Question

How many sides does a regular polygon have if each to its interior angles is 165​

Answer 1

Answer:

Since the measure of each interior angle is 165

Thus, when the regular polygon have if each of its interior angle is 165° then,

The corresponding exterior angle must be 180-165 = 15°

The sum of ALL the exterior angles is 360°

Sides of exterior angles is 360/15 = 24

Therefore the number of sides a regular polygon will have is 24

hope this helps!

Answer 2

Answer:

Since the measure of each interior angle is {eq}165^\circ, {/eq} we have $$\begin{align} \dfrac{180^\circ(n-2)}{n}&= 165^\circ\\ 180^\circ(n-2) &= 165^\circ n\\ 180^\circ n -360^\circ &= 165^\circ n\\ 180^\circ n -165^\circ n &= 360^\circ\\ 15^\circ n &= 360^\circ\\ n&= 24 \end{align}}