How many sides has a regular polygon whose interior angle is 135°?
The correct answer is D. 8
A regular polygon with an interior angle of 135° has 8 sides.
The formula for the interior angle of a regular polygon is
\(\frac{(n-2) \times 180^\circ}{n}\), where n is the number of sides.
If we let the interior angle be 135°, we can solve for n: \(\frac{(n-2) \times 180^\circ}{n} = 135^\circ\).
This simplifies to \(180n - 360 = 135n\), which further
simplifies to:
\(45n = 360\).
Dividing both sides by 45, we get \(n = 8\). Therefore, a regular polygon with an interior angle of 135° has 8 sides.
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