Question

In the adjoining figure, ABCD is parallelogram. Find values of x, y and z.

Answer 1

Explanation:

z= 180-50-102 = 28

y = 50+120 = 170

Answer 2

x = 3

∠y = 152∘

∠z = 28∘

Explanation:

Given: ABCD is parallelogram.

Opposite sides of a parallelogram are equal.

So 2x + 2 = 3x - 1

x = 3.

Opposite angles of a parallelogram are equal.

∠B = ∠D = 102∘

In △ADC, ∠y = 50∘ + ∠D (Ext. angle property of  △)

∠y = 50∘ + 102∘ = 152∘

Again, ∠D + ∠A = 180∘

50∘ + ∠z +102∘ = 180∘

∠z = 28∘.

Hence solved.