Question

How many degrees are in each interior angle of a regular pentagon? 50 72 108 120

Answer 1

The answer 108 degrees.

Answer 2

Answer:
`108^(\circ)`

Explanation:

The sum of all the angles in a regular polygon with sides n , is given by :-

`S_n=180^(\circ)(n-2)`

Now, the sum of all the angles in a regular pentagon with 5 sides will be :-

`S_5=180^(\circ)(5-2)=180^(\circ)(3)=540^(\circ)`

We know that all the interior angles of a regular polygon are equal .

Therefore, the measure of each interior angle in a pentagon is given by :-

`x=(540^(\circ))/(5)=108^(\circ)`

Hence, the measure of each interior angle in a pentagon=
`108^(\circ)`