Question

Find in radians the angles of a regular polygon of 12 sides.

Answer 1

Answer:

Now as we know that a regular dodecagon means a polygon with 12 sides and 12 angles and each of the sides and angles are equal to each other.

⇒⇒For a regular dodecagon ‘n’ = 12

We know that the measure of each interior angle of a regular polygon having ‘n’ sides is given by as follows:

Each angle =(n−2n)×180=(n−2n)×180 degree

So for a regular dodecagon, each angle =(12−212)×180=(12−212)×180 degree

=1012×180=1012×180 degree

=56×180=56×180 degree = 150 degrees

We know that 1 degree =π180=π180 radians

⇒150∘=π180×150⇒150∘=π180×150 radians

=5π6=5π6 radians

Therefore, the magnitude of interior angles of a regular dodecagon in radians and degrees are 5π65π6 radians and 150150 degree respectively.