Question

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

Answer 1

SOLUTION

TO DETERMINE

The number of sides a regular polygon if each of its interior angles is 165°

CONCEPT TO BE IMPLEMENTED

The sum of exterior angles of any polygon is 360°

EVALUATION

Here it is given that each of the interior angles of the regular polygon is 165°

So each of the exterior angles of the regular polygon is

= 180° - 165°

= 15°

Now we know that the sum of exterior angles of any polygon is 360°

So the required number of sides

$\displaystyle \sf{ = \frac{360}{15} \: }$

$= \sf{24 \: }$

FINAL ANSWER

The number of sides a regular polygon if each of its interior angles is 165° = 24

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