A Pentagon has an interior angle of 108 degrees.
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That's true if the interior angles are 108 degrees, but a regular polygon cannot have exterior angles of 108 degrees.
There are 5 interior angles and each one measures 108 degrees (180-72). Since the sum of exterior angles of any polygon is 360⁰, then that polygon would have 5 angles (360/72). So the sum of interior angle measures is 540⁰.
Interior angles are 108o. 360 - 108 = 252o for each exterior angle * * * * * Each exterior angle is 360/5 = 72 degrees, NOT 252. The 108 for the interior angle is correct, but to get from interior to exterior you subtract from 180, not 360!
The total of the interior angles of a pentagon = 540 (in a regular pentagon, each interior angle is 108 degrees). The exterior angles would then be 5*(360-108) = 5*252 = 1260 degrees.
The sum of the interior angles in a pentagon is (5-2)180 degrees or 3x180 degrees=540. Since it is regular each angle has the same measure and so each is 540/5=108 degrees.