Question

find the measure of each exterior angle of a regular polygon of 15 sides

Answer 1

For a n-sided regular polygon, sum of internal angles = (n-2)×180°

Since all internal angles are equal, the internal angle can is given as:

$\alpha = ( \frac{n - 2}{n} ) \times {180}^{o}$

Here, it is given that the polygon has 15 sides.

So n = 15


$\alpha = ( \frac{15 - 2}{15} ) \times {180}^{o} = \frac{13 \times 180}{15} = 156^{o}$

So each internal angle is 156°.

Internal and external angle are always supplementary. So sum of the internal and external angle is 180°.

So external angle = 180° - 156° = 24°.

Measure of each external angle is 24°.

Answer 2

Answer:

The measure of an exterior angle of a regular polygon of 15 sides is 24°.        

Step-by-step explanation:

Given the number of sides of regular polygon, n = 15

The sum of the exterior angles of a regular polygon is 360°.

Regular polygon:

• If all the sides and interior angles of the polygons are equal, they are known as regular polygons.
• In a polygon, each of the exterior angles are equal.
• In n-sided regular polygon, the measure of each interior angle is given by

       $\dfrac{(n -2) \times 180^o}{n}$

• In n-sided regular polygon, the measure of each exterior angle is $360^o/n$

Therefore, the measure of exterior angle of the given polygon is

$\dfrac{360}{15} =24^o$

Therefore, the measure of an exterior angle of a regular polygon of 15 sides is 24°.