An interior angle of a regular polygon has a measure of `108^@`. What type of polygon is it?

Explanation

It is given that:
One interior angle of a regular polygon `= 108^@`
The sum of interior angles of a regular polygon `= (n - 2) × 180^@`
The interior angle of a regular polygon` = [(n - 2) × 180^@]/n`
By equating both we get
`108 = [(n - 2) × 180^0]/n`
By further simplification
`108n = 180n - 360`
`180n - 108n = 360`
So we get
`72n = 360`
`n = 5`
Therefore, it is a 5 sided polygon known as pentagon.