Question

how many sides does a regular polygon have if each of its interior angle in 135°​

Answer 1

Answer:

All sides are the same length (congruent) and all interior angles are the same size (congruent). To find the measure of the angles, we know that the sum of all the angles is 1080 degrees (from above)... And there are eight angles... So, the measure of the interior angle of a regular octagon is 135 degrees.

Answer 2

Answer:

Interior angles + exterior angles = 180 degree

find exterior angle

135 + exterior angles = 180

exterior angles = 180 -135

exterior angles = 45 degrees

find the number of sides

sum of all exterior angles = 360 degree

number of sides = 360 ÷45 = 8 sides