Question

If each interior angle of a regular polygon is 10 times its exterior angle, then the number of sides of polygon is
A) 12
B) 18
C) 22
D) 24

Answer 1

Hint:
It is given in the question that if each interior angle of a regular polygon is 10 times its exterior angle.
Then, we have to find the number of sides of the polygon.
The sum of interior angles of a regular polygon $ = \left( {n - 2} \right)180^\circ $ and the sum of exterior angles of regular polygon $ = 360^\circ $
By the above information, we will get the answer.

Complete step by step solution:
It is given in the question that if each interior angle of a regular polygon is 10 times its exterior angle.
Then, we have to find the number of sides of the polygon.
Since, the sum of interior angles of a regular polygon $ = \left( {n - 2} \right)180^\circ $
The sum of exterior angles of regular polygon $ = 360^\circ $
Now, it is given in the question that the interior angle of a regular polygon is 10 times its exterior angle.
$\therefore $sum of interior angle =10 $ \times $ sum of exterior angle
 $\therefore \left( {n - 2} \right)180^\circ = 10 \times 360^\circ $
 $\therefore \left( {n - 2} \right) = \dfrac{{10 \times 360}}{{180}}$
 $\therefore n - 2 = 20$
 $\therefore n = 22$

Therefore, the number of sides of a polygon is 22.

Note:
Regular Polygon: A regular polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length). Regular polygon may be either convex or star. A regular n-sided polygon has rotational symmetry of order n.
All vertices of a regular polygon lie on a common circle i.e. they are concyclic points. That is, a regular polygon is a cyclic polygon.