Question

The deck that Kenneth is building is in the shape of a parallelogram ABCD the measure of angle C is one third the measure of angle B find the measure of each angle of the deck

Answer 1

∠A = ∠C = 45° and ∠B = ∠D = 135°

Explanation:

In the picture attached ABCD is a parallelogram in which the measure of angle C is one third of the measure of angle B.

Since in a parallelogram opposite angle are equal then we can say easily that ∠A = ∠C and ∠B = ∠D

We know in a parallelogram sum of all internal angles = 360°

Therefore ∠A + ∠B +∠C + ∠D = 360°

Since ∠A = ∠C and ∠D = ∠B

∠C + ∠B + ∠C + ∠B = 360°

2(∠B + ∠C) =360

∠B + ∠C = 180

Now ∠C = 1/3×∠B

∠B + 1/3×∠B = 180

4/3 ×(∠B) =180

∠B =
`(3)/(4)(180) = 135`

∠C = 1/3×∠B = 135/3 = 45°

Therefore ∠B = ∠D = 135° and ∠A = ∠C = 45°