A regular polygon with an interior angle of 108 degrees is a pentagon.
To understand why, we can use the formula for the interior angle of a regular polygon:
Interior Angle = (n – 2) × 180° / n
Where n is the number of sides in the polygon. Setting the interior angle equal to 108 degrees, we have:
108 = (n – 2) × 180° / n
Multiplying both sides by n gives:
108n = (n – 2) × 180
Expanding the right side results in:
108n = 180n – 360
Rearranging this gives:
72n = 360
Now, dividing both sides by 72 results in:
n = 5
This means the polygon has 5 sides, which is known as a pentagon. Thus, a regular polygon with an interior angle of 108 degrees is a pentagon.