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.

Yes i also think it is b

38+105= 143, 39+104=143, and you will find then adding the numbers on opposite sides, moving inwards yields the answer 138 every time. because of this, you’re going to multiply 138 times the number of pairs, which is 34. therefore, 34*138= 4692(i’m sorry if it’s the wrong numbers, but it’s the right concept)