Question

The measure of each angle of a polygon is $160^0$. The number of its sides is?
A. 15
B. 18
C. 20
D. 30

Answer 1

Hint:
Firstly, we will assume the number of sides to be $n$. Then, we will substitute the given value in the formula of an interior angle of a polygon. From this we will calculate the number of sides.

Complete step by step solution:
We are given the measure of each interior angle of a polygon to be $160^0$. Now, let’s assume the number of sides of the given polygon to be $n$.
We know that, the formula to calculate the interior angle of a polygon of $n$ sides is given by
$
  Angle = \dfrac{{(n - 2){{180}^0}}}{n} \\
   \Rightarrow {160^o} = \dfrac{{(n - 2){{180}^0}}}{n} \\
   \Rightarrow {160^0}n = 180n - {360^0} \\
   \Rightarrow {180^0}n - {160^0}n = {360^0} \\
   \Rightarrow {20^0}n = {360^0} \\
   \Rightarrow n = \dfrac{{{{360}^0}}}{{{{20}^0}}} \\
   \Rightarrow n = 18 \\
$
So, the given polynomial has 18 sides

Therefore, the right option is B.

Note:
There is an alternate approach to attempt this question using exterior angles.
We are given the interior angle to 1600. We know that Exterior angle of a polygon is given by
(1800-Interior Angle).
So, exterior angle turns out to be ${180^0} - {160^0} = {20^0}$
We also know that the sum of all exterior angles of a polygon is 360 degrees. Hence, the total no. of exterior angles in the given problem can be found as following:
$\dfrac{{{{360}^0}}}{{{{20}^0}}} = 18$
SO, there are 18 angles in for the given polygon. And it is also known that every polygon has an equal number of sides and angles.
Hence, we conclude that the given polygon has 18 sides.
The correct option is B.