Question

The window frame is a regular octagon. It is made from eight pieces of wood shaped like congruent isosceles trapezoids . What are m angle A , m angle B.m angle C and m angle D ?

Answer 1

∠A= 112.5°, ∠B=67.5°, ∠C is 67.5° and ∠D 112.5°.

Explanation:

Consider the provided information.

The sum of all interior angle of a polygon is:
`(n-2)180`

Substitute n = 8.

`(8-2)180=1080`

Thus, the measure of each angle is:
`(1080)/(8)=135`

∠B and ∠C are congruent and their sum is 135°

∠B+∠C=135°

∠B=67.5°

Hence, the m angle B and m angle C is 67.5°.

The sum of all angles of a quadrilateral is 360°.

∠A+∠D+∠B+∠C=360°

∠A+∠D=360°-135°

∠A+∠D=225°

∠A and ∠D are congruent and their sum is 225°

∠A+∠D=225°

∠A=∠D=112.5°

Hence, the m angle A and m angle D is 112.5°.