How many sides has a regular polygon whose interior angle is 135o
Answer Details
The formula to find the interior angle of a regular polygon is:
Interior angle = (n - 2) × 180° / n
Where "n" is the number of sides of the polygon.
We are given that the interior angle of the regular polygon is 135°, so we can substitute this value into the formula and solve for "n":
135 = (n - 2) × 180° / n
Multiplying both sides by "n":
135n = (n - 2) × 180°
Distributing on the right-hand side:
135n = 180n - 360°
Subtracting 135n from both sides:
0 = 45n - 360°
Adding 360° to both sides:
360° = 45n
Dividing both sides by 45:
8 = n
So the regular polygon has 8 sides.
Looking at the given answer options, we see that the answer is (D) 8.