Question

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

Explanation:

Step1: Find the measure of an 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