Question

The centre of the stained glass window is in the shape of a regular polygon. What are the measures of the interior angle of the green triangle?

CAN SOMEONE EXPLAIN WITH REASONING STEP BY STEP Solution so I can grasp the concept easily. please explain with a sol

Answer 1

67.5 - 67.5 - 45 °

Explanation:

Sum of INTERIOR angles of a polygon

(n-2) * 180 <====ya just have to remember/know this !

n is the number of sides n = 8 in this case

(8-2)*180 = 1080 ° < === this is the SUM of the 8 interior angles

EACH interior angle is then 1080 / 8 = 135 °

you can see from the picture that each of the two outside angles of the green triangle are 1/2 of this = 67.5° each

so the triangle measurements are

67.5 - 67.5 - 45 ( they have to sum to 180 for triangle)