Question

No of sides of a polygon having each angle as 30 degree.

Answer 1

Hey dear!

Given,
Each angle of polygon = 30°

Now,
We know that,
Sum of all interior angles of polygon = (2x-4)×90°

[Here x = Number Of Sides]

Now,

(2x-4)×90°= 30x
$2x - 4 = \frac{30x}{90}$
$2x - 4 = \frac{x}{3}$
$6x - 12 = x$
$6x = x + 12$
$6x - x = 12$
$5x = 12$
$x = \frac{12}{5}$
Since,
Number of sides is not a real number. Polygon is not possible with each interior angle 30°.