An interior angle of a regular polygon has a measure of 135°. what type of polygon is it?

hexagon
octagon
nonagon
decagon

1.       The sum of the measures of the interior angles of a (convex) polygon is (n-2)∙180°, where n is the number of sides.

2.       For example, for n=4, a quadrilateral, the sum of the interior angle measures is:

(n-2)∙180°=(4-2)∙180°=2∙180°=360°

Similarly, for n=5, a pentagon, the sum of the interior angles is 

(n-2)∙180°=(5-2)∙180°=3∙180°=540°

Now in a regular polygon, the measure of each angle is same, so the total sum (n-2)∙180° is distributed equaly, thus the measure of 1 angle of a regular polygon is 

 \frac{(n-2)180^o}{n} 

4.So we solve the following equation:

Which means the polygon is an octagon, from “octa”, meaning 8 in ancient greek.

answer: ask

step-by-step explanation:

explanation:

step-by-step explanation: