Question

how many sides in a regular polygon has if each of its interior angle is 135 degree

Answer 1

"Because the octagon is regular, all of its sides and angles are congruent. Thus, the measure of each angle is equal to the sum of its angles divided by 8. Therefore, each angle in thepolygon has a measure of 1080/8 =135 degrees. This means that angleFHG has a measure of 135 degrees."

Answer 2

Interior angle + exterior angle = 180º

FInd exterior angle:

135 + exterior angle = 180

exterior angle = 180 - 135

exterior angle = 45º

Find the number of sides:

Sum of all exterior angles = 360º

Number of sides = 360 ÷ 45 = 8 sides

Answer: It is a 8-sided polygon