Question

The interior angle of regular polygon is 156 degree. find the number of sides of the polygon

Answer 1

Hi,

Interior angle= 156°
Exterior angle = 180-156= 24°

No. of sides = 360/exterior angle
= 360/24
= 15sides

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Answer 2

Given:

The interior angle of a regular polygon is 156 degrees.

To find:

The number of sides of the polygon.

Solution:

If the interior angle of a regular polygon is 156 degrees then the number of sides of the polygon is 15.

We can solve the above mathematical problem using the following approach.

The sum of an interior angle and an exterior angle is 180°, so if the interior angle is 156°, then the exterior angle = 180° - 156° = 24°.

In a regular polygon, the sum of all the exterior angles lying in the polygon adds up to 360°.

In order to find out the number of sides of the polygon, we divide 360° by 24° = $\frac{360^\circ}{24^\circ} = 15.$

Therefore, the number of sides of the polygon is 15.