an interior angle of a regular polygon has a measure of 135°. what type of polygon is it?\nhexagon\noctagon\n…

Answer:

B. octagon

Explanation:

Step1: Find the exterior - angle

The sum of an interior angle and an exterior angle of a polygon is 180°. Given the interior angle is 135°, so the exterior angle $\theta=180 - 135=45^{\circ}$.

Step2: Use the formula for the number of sides

The sum of exterior angles of any polygon is 360°. Let the number of sides of the polygon be $n$. We know that $n=\frac{360}{\text{exterior - angle}}$. Substituting the value of the exterior angle $\theta = 45^{\circ}$, we get $n=\frac{360}{45}=8$. A polygon with 8 sides is an octagon.