Question

In the adjoining figure , ABCD is a parallelogram. Find the values of X,Y,Z ​

Answer 1

Answer:

x = 3

∠y = 152∘

∠z = 28∘

Step-by-step 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∘

so..

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.

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Answer 2

Answer:

X = 3; Y = 152°; Z = 28°

Step-by-step explanation:

Since Opposite sides of a Parallelogram are equal,

=> 2x+2 = 3x-1

=> 2x-3x = -1 -2 [Transposition]

=> -x = -3

Therefore, X = 3 [minus sign gets cancelled]

∠CBA+∠DAB = 180° [Adjencent angles of Parallelogram are equal] So,

=> 102°+50+z = 180°

=> 152+z = 180

=> z = 180-152 [Transposition]

Therefore, Z = 28°

∠DCA = z [Alternate Interior Angles, as DC is Parallel to AB]

∠DCA = 28°

=> ∠DCA+y = 180° [Linear Pair]

=> 28+y = 180

=> y = 180-28

Therefore, Y = 152°

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