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Question

In the given figures, PQRS is a parallelogram .Find the value of x,y and z.
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Solution

In figure (i),

PAS+SAR=180 . . . [Linear pair of angles]

x=18090

x=90


In SAR,

y=180(90+40) . . . [Angle sum property]

y=50


In parallelogram PQRS,

PSR=2×ASR

PSR=100

So PQR=100 [opposite angles]

And hence z=50


In figure (ii),

x=110 [opposite angle of parallelogram are equal]


and x+z=180 [alternate interior angles]

z=70


Also y+z=180 [linear pair of angles]

y=110


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