Each interior angle of a regular polygon is 156- Find the number of sides of the polygon-

Let there be n sides of the polygon. Then, its each interior angle is equal to (n 2)×180n=156 ⇒ 180n – 360 = 156n ⇒ 24n = 360 ⇒ n = 15 Thus, there are 15 si ...

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Standard VIII

Mathematics

Deducing a Formula for Sum of Interior Angles of a Polygon

Each interior...

Question

Each interior angle of a regular polygon is 156 $^{\circ}$ . Find the number of sides of the polygon.

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Solution

Let there be n sides of the polygon.
Then, its each interior angle is equal to $\frac{(n - 2) \times 180}{n} = 156$

$\Rightarrow 180 n - 360 = 156 n$

$\Rightarrow 24 n = 360$

$\Rightarrow n = 15$

Thus, there are 15 sides of the polygon.

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Each interior angle of a regular polygon is 156∘. Find the number of sides of the polygon.

Let there be n sides of the polygon. Then, its each interior angle is equal to (n−2)×180n=156 ⇒180n–360=156n ⇒24n=360 ⇒n=15 Thus, there are 15 sides of the polygon.

Each interior angle of a regular polygon is 156 $^{\circ}$ . Find the number of sides of the polygon.

Let there be n sides of the polygon.
Then, its each interior angle is equal to $\frac{(n - 2) \times 180}{n} = 156$

$\Rightarrow 180 n - 360 = 156 n$

$\Rightarrow 24 n = 360$

$\Rightarrow n = 15$

Thus, there are 15 sides of the polygon.