an interior angle of a regular polygon has a measure of 135°. what type of polygon is it? hexagon octagon…

Explanation:

Step1: Find the measure of the exterior angle

The sum of an interior angle and its corresponding exterior angle of a polygon is (180^{\circ}). If the interior angle is (135^{\circ}), then the exterior angle (e = 180^{\circ}- 135^{\circ}=45^{\circ})

Step2: Use the formula for the number of sides of a regular polygon

The sum of all exterior angles of a polygon is (360^{\circ}). For a regular polygon with (n) sides, (n=\frac{360^{\circ}}{e}) (where (e) is the measure of one exterior angle) Substitute (e = 45^{\circ}) into the formula: (n=\frac{360^{\circ}}{45^{\circ}} = 8)

Answer:

octagon