Question

How many sides does a regular polygon have if each of its interior angles is 165 degree?

Answer 1

Hint: We know that in a regular polygon if the interior angle is x then the exterior angle is (180-x) because it forms a linear pair.

Complete step-by-step answer:
Similarly in this question
Interior angle, x=165 degree
Therefore exterior angle = (180-x)
$
   = \left( {180^\circ - 165^\circ } \right) \\
   = 15^\circ \\
$
Also we know that the sum of all exterior angles of any polygon is 360 degree
Therefore number of sides $ = \dfrac{{360^\circ }}{{{\text{each exterior angle}}}}$
$ = \dfrac{{360^\circ }}{{{15^\circ}}}$
 = 24

Hence the number of sides a regular polygon has if its interior angle is 165 degrees are 24.

Note: We know that the sum of all exterior angles in any polygon is 360 degree. Dividing this 360 degree from each exterior angle gives the number of sides it would have, so first we found the exterior angle by linear pair after that we calculated the number of sides.