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Question

In the given figure, if AB || CD || EF, PQ || RS, RQD=25 and CQP=60, then QRS is equal to

  1. 85
  2. 135
  3. 145
  4. 110


Solution

The correct option is C 145
We have PQ || RS. Produce PQ to M.
CQP=MQD    [Vertically opp. S]
60=1+25
1=35
Now, QM || RS and QR cuts CD and AB
ARQ=RQD=25       [Alt. S]
1+(ARQ+RMP)=180
1+(ARQ+ARS)=180
35+(25+ARS)=180
ARS=18060=120
QRS=ARQ+ARS
=25+120=145

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