Question

find the no sides of a regular polygon when each of its interior angle measure 150​

Answer 1

Answer:

12 sides (Dodecagon).

Step-by-step explanation:

If the interior angle is $\theta$, then the number of sides is given by the formula:

$n = \frac{360^o}{180^o - \theta}$ *

Here, $\theta = 150^o$

So, $n = \frac{360^o}{180^o - 150^o} = \frac{360^o}{30^o} = 12$

* In terms of radians, the formula shall be: $n = \frac{2\pi}{\pi - \theta}$

Derivation (when angle is in degrees):

If the interior angle is $\theta$, then the exterior angle is $180^o - \theta$.

Also, the sum of exterior angles of a polygon is always $360^o$.

Let n be the number of sides of the polygon.

So, $n * (180^o - \theta) = 360^o$

And finally, $n = \frac{360^o}{180^o - \theta}$

There is a slightly more involved, but easily understandable explanation. If you're in 9th or above, and want the explanation, kindly comment below.

Answer 2

Use the formula (n-2)*180=sum of all interior angles

Now (n-2)*180=150n n means no of sides 180n-360=150n so n=12