Question

ABCD is a parallelogram find the value of x and y mention the property used.​

Answer 1

Answer:

x= 30 , y=100

Step-by-step explanation:

ABCD is a parallelogram, with diagonals AC and BD intersect at point O.

⇒  ∠A+∠B=180  o

         [ Sum of adjacent angles are supplementary in parallel ]

⇒  110  o +(40  o  +x)=180  o

 ⇒  150  o  +x=180  o

 ⇒  x=30  o

 In △OBC,

⇒  ∠OBC+∠BCO+∠COB=180  o

 ⇒  x+50  o  +y=180  o

 ⇒  30  o  +50  o +y=180  o

 ⇒  80  o +y=180  o

 ∴  y=100  o

 ∴  x=30  o  ,y=100  o

Answer 2

Answer:

Let us mark the mid point of the parellelogram as point O

GIVEN,

angle BAD = 110°

angle ABD = 40°

and angle BCD =50°

PROOF,

In ∆ DBA

angle BAD + angle ABD + angle ADB = 180° [ Angle Sum Property of a ∆]

> > 110° + 40° + angle ADB = 180°

>> angle ADB = 180° - 150°

>> angle ADB = 30°

angle ADB = angle DBC [ Alternate Interior Angles]

>> 30° = angle DBC

>> 30° = x

In ∆ BOC

angle OBC + angle BCO + angle COB = 180° [ Angle Sum Property of a ∆ ]

>> 30° + 50° + angle COB = 180°

>> angle COB = 180° - 80°

>> angle COB = 100°

>> y = 100°

Step-by-step explanation:

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