Question

HOW MANY SIDES DOES A REGULAR POLYGON HAVE IF EACH OF ITS INTERIOR ANGLES IS 165 ?

Answer 1

Hello!!

Here is your answer.

Given that one of the interior angle = 165°.

We know that Sum of interior and exterior angles of a polygon = 180°.

So, Exterior angle = 180° - 165°
= 15°.

So, exterior angle of that polygon = 15°.

We also know that sum of exterior angles of a polygon is always 360°.
So,
Number of sides = $\frac{360}{15} \\ = 24 \: sides$

Hence the number of sides = 24.

Hope You Got It

Answer 2

Answer:

24 sides

Explanation:

180° - 165° = 15°.

[Linear pair]

Exterior angle of that polygon = 15°.

Sum of exterior angles of a polygon is always 360°.

Number of sides = $\frac{360}{15}$ = 24 sides