Question

Each Interior angle of a regular polygon is 174. Work out the number of sides of the
polygon​

Answer 1

Answer:

The polygon has 60 sides.

Step-by-step explanation:

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Answer 2

Given : The each interior angle of a regular polygon is 174°

To find : The number of sides of the polygon.

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to calculate the number of sides of the polygon)

Now, the sum of an interior angle and an exterior angle of a regular polygon is always equal to 180°.

So, the exterior angle of the given regular polygon :

= (Sum of an interior angle and an exterior angle) - (An interior angle)

= 180° - 174°

= 6°

Let, the number of sides of the regular polygon = n

Now, value of an exterior angle of a regular polygon = (360° / Number of sides)

So, the an exterior angle of the given regular polygon :

= (360°/n)

By, comparing the two values of an exterior angle of the given regular polygon, we get :

360/n = 6

n × 6 = 360

n = 360/6

n = 60

Number of sides of the regular polygon = n = 60

(This will be considered as the final result.)

Hence, the number of the sides of the regular polygon is 60