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Q.

In the given figure ABCD is a parallelogram. Find the angles x and y.https://www.vedantu.com/question-sets/bdbb9b79-f1a0-4ea4-8d2e-ac5423fff9eb2835629953320962212.png


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a

60°, 40°

b

30°, 30°

c

40°, 70°

d

60°, 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°
60°+y = 100°
⇒y = 100 −60 = 40°
So,
x = 60°
y = 40°
 
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In the given figure ABCD is a parallelogram. Find the angles x and y.