Question

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

Answer 1

24 sides.

Complete step-by-step answer:

We are given that each of the interior angles of a regular polygon is 165∘

.

Let us assume that the number of sides of a regular polygon is represented by n

.

We know that the measure of each interior angle of a regular polygon the formula is given by 180∘(n−2)n

.

Since the measure of each interior angle is 165∘

, we have

⇒180∘(n−2)n=165∘

Multiplying the above equation by n

on both sides, we get

⇒180∘(n−2)=165∘n⇒180∘n−360∘=165∘n

Adding the above equation with 360∘

on each side, we get

⇒180∘n−360∘+360∘=165∘n+360∘⇒180∘n=165∘n+360∘

Subtracting both sides by 165∘n

on both sides, we get

⇒180∘n−165∘n=165∘n+360∘−165∘n⇒15∘n=360∘

Dividing the above equation by 15∘

on each side, we get

⇒15∘n15∘=360∘15∘⇒n=24∘

Thus, the regular polygon with interior angle each measuring 165∘

is a 24-sided polygon.

Hence, our option A is correct.

Note: We have to always remember that the sum of all the exterior angles in any polygon is 360 degree. In solving these types of questions, we have to take the given angle of a regular polygon equal to 180∘(n−2)n

. Then this question will be very simple to solve and compute the value of n.

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