Question

In parallelogram ABCD, ZA = ZB + 50°,
then find the measure of each angle of the
quadrilateral ABCD.​

Answer 1

Let angle B be x, then angle A = angle B +50 = x +50.
Now, in a parallelogram, the opposite angles are equal.
Thus, angle A = angle C = x+50 & similarly angle B = angle D = x .
We know that the sum of all angles of a parallelogram (or an quadrilateral) equals 360. Now this means,
angle A + angle B + angle C + angle D = 360
On substituting the values, we get,
x+50 + x + x+50 + x = 360
4x + 100 = 360
4x = 360 — 100 = 260
x = 260/4 = 65
Thus, angle A = x+50 = 65+50 = 115
angle B = x = 65
angle C = x+50 = 115
angle D = x = 65