Question

how many sides does a regular polygon have if each of its interior angles is 150 degree

Answer 1

List all possibilities of all polygons which can have 150 degrees as interior angles

Answer 2

Solution :-

Given :-

• Interior angles of regular polygon is 150°.

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 = 150n

=> 180n - 360 = 150n

=> 180n - 150n = 360 => 30 = 360

$= > \: n \: = \frac{360}{30} = 12$

∴ the polygon has 12 sides.

Alternate Method :

Each exterior angle = 180° - 150° = 30°

Let n be the number of sides.

n × 30° = 360° ( exterior angle sum property)

$So, n = \frac{360}{30} = 12$

Thus, the polygon has 12 sides.