The interior angle of a regular polygon is $156$ . Find the number of sides of the polygon.

Given: The interior angle of a  regular polygon is $156$

To do: Find the number of sides of the polygon

Answer:

The sum of interior angles of a regular polygon of n sides is given by $(n - 2)180°$

Given an angle of the regular polygon = $156°$

Sum of angles of the polygon = $156n = (n  - 2) $\times$ 180°$

$180n - 360 = 156n$

$180n - 156n = 360°$

$24n = 360°$

n = $\frac{360}{24}$ = 15

So the required polygon has 15 sides.

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Updated on: 10-Oct-2022

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