Desirae Kirby

2023-03-14

How many sides does a regular polygon have if the measure of an exterior angle is $24\xb0$?

Ligurischjz1

Beginner2023-03-15Added 4 answers

To determine the number of sides, use the polygon's exterior angle sum property:

It is given that a regular polygon has the measure of an exterior angle $24\xb0$.

Since according to the exterior angle sum property of the polygon,

(number of sides) $\times $(the measure of each exterior angle) $=360\xb0$[Using exterior angle property]

$\Rightarrow $ (number of sides) $\times $$24\xb0=360\xb0$

$\Rightarrow $ Number of sides $=\frac{360\xb0}{24\xb0}$

$\Rightarrow $$=15$

Hence, the polygon has $15$sides.

It is given that a regular polygon has the measure of an exterior angle $24\xb0$.

Since according to the exterior angle sum property of the polygon,

(number of sides) $\times $(the measure of each exterior angle) $=360\xb0$[Using exterior angle property]

$\Rightarrow $ (number of sides) $\times $$24\xb0=360\xb0$

$\Rightarrow $ Number of sides $=\frac{360\xb0}{24\xb0}$

$\Rightarrow $$=15$

Hence, the polygon has $15$sides.