Answer:
∠A = ∠C = 45° and ∠B = ∠D = 135°
Step-by-step 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 = [tex]\frac{3}{4}(180) = 135[/tex]
∠C = 1/3×∠B = 135/3 = 45°
Therefore ∠B = ∠D = 135° and ∠A = ∠C = 45°
