Can a regular polygon have an interior angle of 132 degrees?

Given:

The interior angle of a regular polygon is 132 degrees.

To find:

The given statement is possible or not.

Solution:

Let as assume the interior angle of a regular polygon with n vertices is 132 degrees.

Then, the exterior angles are

We have, n vertices. So, the number of exterior angles is n.

Sum of all exterior angles = 48n degrees

We know that, sum of all exterior angles of a regular polygon is always 360 degrees.

Number of vertices is always a whole number. So, it cannot be a fraction value.

So, our assumption is wrong.

Therefore, a regular polygon cannot have an interior angle of 132 degrees.

7 ft 6 in means 7 1/2, because 6 in is 1/2 of a foot. 7 ft 8 in means 7 2/3 because 8 in is 2/3 of a foot. 23/3 = 7 2/3. 15/2 = 7 1/2.

23/3   *   15/2   = 57 1/2

step-by-step explanation: