To determine what type of polygon has an interior angle of 135 degrees, we can use the formula for finding the measure of an interior angle of a regular polygon. The formula is:
Interior Angle = (n – 2) * 180° / n
Here, n represents the number of sides in the polygon. We can rearrange this formula to solve for n when we know the interior angle.
Substituting the known interior angle into the formula:
135° = (n – 2) * 180° / n
Multiplying both sides by n to eliminate the fraction, we get:
135n = (n – 2) * 180
Expanding this gives:
135n = 180n – 360
Now, we can isolate n by moving 180n to the left side:
135n – 180n = -360
-45n = -360
Now, dividing both sides by -45:
n = 8
This means that the polygon has 8 sides, which is known as an octagon. Therefore, a regular polygon with an interior angle of 135 degrees is an octagon.