Question

how many sides does a regular polygon have if the each of its interior angles is 165°?​

Answer 1

Answer:

A/q

Measure of interior angles = 165°

So, exterior angle = (180-165)° = 15°

No. of sides = 360/exterior angle

= 360/ 15

= 24

Hence, a regular polygon with interior angle 165° will have 24 sides.

Answer 2

Answer:

we know that

In a linear pair the interior and exterior angles make 180°

180 - 165 = 15° [ one of the exterior angle ]

We also know that

Sum of the exterior angles in any regular polygon is 360°

360 / 15 = 24 exterior angles

No. of exterior angles = no. of interior angles = no of sides in any regular polygon

:. 24 sides in this regular polygon.