Question

in the following figure both ABCD and PQRS are parallelogram. find the value of x​

Answer 1

Step-by-step explanation:

In parallelogram ABCD,

∠A=∠C=120

o

[opposite angles of a parallelogram are equal]

and ∠DCB+∠SCO=180

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[Linear pair]

∠SCO=180−120=60

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...(1)

Now, in parallelogram PQRS,

∠S+∠R=180

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[adjacent angles of parallelogram]

∠RSP=180−50=130

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and ∠RSP+∠CSO=180

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[linear pair]

∠CSO=180−130=50

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...(2)

Now In ΔCOS,

∠COS+∠OCS+∠CSO=180

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[angle sum proportion]

∠COS=180−50−60 [From equation (1) & (2)]

∠COS=70

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Hence ∠COS=∠POB [vertically opposite angles]

⇒x=70

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Therefore the value of x is 70

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