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In figure, if AB |""| CD |""| EF, PQ |""...

In figure, if AB `|""|` CD `|""|` EF, PQ `|""|` RS, `/_` RQD =`25^(@)` and `/_` CQP =`60^(@)`, then `/_`QRS is equal to

A

`85^(@)`

B

`135^(@)`

C

`145^(@)`

D

`110^(@)`

Text Solution

Verified by Experts

The correct Answer is:
C
`:. " "/_PQC = /_BRS = 60^(@) " " ["alternate interior angles and" /_PQC = 60^(@)` ("given")]
and `/_QDR = /_QRA = 25^(@) " " ["alternate interior angles"] " "[:'/_DQR = 25^(@)`, given]
`:." "/_QRS = /_QRA +/_ARS`
=`/_QRA + (180^(@)-/_BRS) " "` ["linear pair axiom"]
= `25^(@) + 180^(@) - 60^(@) = 205^(@) - 60^(@) = 145^(@)`
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