Question

A regular polygon has 15 sides. The difference between its interior and exterior angles is​

Answer 1

Answer:

interior angles rjrjrkdmdms

Answer 2

Answer:

The difference between its interior and exterior angles is ${132}^{o}$

Step-by-step explanation:

Given,a regular polygon has 15 sides.

Here we want to find what is difference between its interior and exterior angles ?

But now question is how can we find interior and exterior angles of a polygon.

Let a polygon has n number of sides.

Then, value of exterior angle of the polygon is $\frac{ {360}^{o} }{n}$

and value of interior angle of the polygon is

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

Here value of n is 15.

So, value of one exterior angle of the polygon is

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

Value of one interior angle of the polygon is

$\frac{(15 - 2) \times {180}^{o} }{15} \\ = \frac{13 \times {180}^{o} }{15} \\ = 13 \times {12}^{o} \\ = {156}^{o}$

So difference between exterior and interior angle of the polygon

$= {156}^{o} - {24}^{o} \\ = {132}^{o}$

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