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In the given figure ABCD is a parallelogram. Find the angles x and y.

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°

, 40

°

°

, 30

°

°

, 70

°

°

, 80

°

answer is A.

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Detailed Solution

∠ABD = x

°

(Given)
∠ADB = y

°

(Given)
∠DBC = 40

°

(Given)
∠DAB = 80

°

(Given)
∠DAB+∠ABC=180

°

−−−−(1) (angle sum property of the parallelogram)
As ∠ABC can be written as the sum of two angles which are ∠ABD and ∠DBC
∠DAB+(∠ABD+∠DBC)= 180

°

80+x+40=180

°

⇒ x = 60

°

⇒ ∠DAB+∠ABD+∠ADB=180

°

−−−(2) (angle sum property of triangle)
Hence,
∠DAB=80

°

⇒ 80

°

+∠ABD+∠ADB= 180

°

⇒ ∠ABD+∠ADB=100

°

−−−−−(3)
∠ABD = x = 60

°

⇒∠ADB = y

°

°

+y = 100

°

⇒y = 100 −60 = 40

°

So,
x = 60

°

y = 40

°

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