If each interior angle of a regular polygon is 10 times its exterior angle, then the number of sides of polygon is

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answer is C.

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Detailed Solution

Let n be the number of the sides of the regular polygon.
Let us denote exterior be Ae
Therefore, Exterior angle Ae is =

\frac{360}{n}

And let the interior angle be Ai
Therefore, Exterior angle Ai is =

\frac{n - 2}{n}

× 180
Given that - Each interior angle of a regular polygon is 10 times its exterior angle
Ai = 10 × Ae ∴

\frac{n - 2}{n}

× 180 = 10 ×

\frac{360}{n}

As, same number from both sides of the equations cancels each other, here “n” is cancelled from both sides.
180 (n−2) = 10 × 360
Also, the numerator in the multiplicative part of the left-hand side goes to the denominator of the right-hand side.
n – 2 =

\frac{3600}{180}

Simplify the above equation –
n – 2 = 20
When the number changes its sides, sign of the number changes from positive to negative and vice-t
∴ n = 20 + 2 ∴ n = 22
Therefore, if each interior angle of a regular polygon is 10 times its exterior angle, then the number of sides of the polygon is 22.
Hence, option 3 is correct.

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