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
[tex]180^\circ-132^\circ=48^\circ[/tex]
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.
[tex]48n=360[/tex]
[tex]n=\dfrac{360}{48}[/tex]
[tex]n=7.5[/tex]
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.
