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In the given figure, AB||CD||EF, PQ||RS,...

In the given figure, `AB||CD||EF, PQ||RS, angleRQD=25^(@)` and `angleCQP=60^(@)`. Find `angleQRS`.

Text Solution

Verified by Experts

CD is a line and the ray QP stands on it.
`:. angleCQP+anglePQD=180^(@)`
`implies 60^(@)+anglePQD=180^(@)`
`implies anglePQD=(180^(@)-60^(@))=120^(@)`.
`:. anglePQR=anglePQD+angleRQD=(120^(@)+25^(@))=145^(@)`.
Now, `PQ||RS` and QR is the transversal.
`:. angleQRS=anglePQR=145^(@)` [alternate interior `angles`].
Hence, `angleQRS=145^(@)`.
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