If n is the number of sides, each interior angle I can be calculated by the following formula:
I = 180(n - 2)/n
Substitute:
108 = 180(n - 2)/n
Multiply both sides by n:
108n = 180(n - 2)
Distribute:
108n = 180n - 360
Subtract 180n from both sides:
108n - 180n = -360
Combine like terms:
-72n = -360
Divide both sides by -72:
n = 5
Its a pentagon