Question

how many sides does a regular polygon have if each of its interior angles is 160 degree

Answer 1

If the interior angle of a regular polygon is 160 degrees, then the exterior angle is 20 degrees. The sum of all exterior angles is 360 degrees so there must be 360/20 sides = 18 sides.

Answer 2

Solution :-

Given :-

• Interior angles of regular polygon is 160°.

To Find :-

• How many sides does a regular polygon have?

Step-by-Step-Explaination :-

Let there be n sides of the polygon.

Then,

$Each \: interior \: angles \: = \frac{(n - 2 \times 180° )}{n}$

$Therefore, \frac{(n - 2 \times 180)}{n} = 160$

( n - 2 ) × 180 = 160n

=> 180n - 360 = 160n

=> 180n - 160n = 360 => 20 = 360

$= > \: n \: = \frac{360}{20} = 18$

∴ the polygon has 18 sides.

Alternate Method :

Each exterior angle = 180° - 160° = 20°

Let n be the number of sides.

n × 20° = 360° ( exterior angle sum property)

$So, n = \frac{360}{20} = 18$

Thus, the polygon has 18 sides.