Question

You need to construct a regular polygon. When you draw two sides, the interior angle created between them is 135°, illustrated below.
What will be the sum, in degrees, of the measures of the interior angles of this polygon when it is completed?
ans..

1080°

1440°

720°

900°

Answer 1

135 = interior
45 = exterior

360/45 = 8

Therefore Octagon

Finally 8*135 = 1080

Answer 2

ok so am kinda lost , like where did you get 45 and 360?

Answer 3

Concept #1: Interior and Exterior Angles of a Polygon Are Supplementary, meaning they add to 180 degrees.

interior = x
exterior = y

x + y = 180

135 + y = 180

y = 180 - 135
y = 45

Concept #2: The sum of all exterior angles of a polygon is 360 degrees.
Concept #3: The number of exterior angles is equal to the number of sides

Therefore, if you divide the sum of the exterior angles by the measure of one exterior angle, you should get the number of sides

Therefore, 360/45 = 8

Any questions?

Answer 4

ohh ok i get it now, thank you