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In the given figure, PQbotPS,PQ||SR,angl...

In the given figure, `PQbotPS,PQ||SR,angleSQR=28^(@)andangleQRT=70^(@)."If "anglePQS=x^(@)andanglePSQ=y^(@)`, find the values of x and y.

Text Solution

Verified by Experts

`PQ||SRTandQR` is a transversal.
`:.anglePQP=angleQRT" "["alternate intreior angles"]`
`impliesanglePQS+angleSQR=angleQRT`
`impliesx+28=70`
`impliesx=(70-28)=42`.
In right `DeltaPQS`, we have
`angleSPQ+anglePQS+angleQSP=180^(@)`
[sum of the angles of a `Delta" is "180^(@)`]
`implies90^(@)+x^(@)+y^(@)=180^(@)`
`impliesx^(@)+y^(@)=90^(@)implies42+y=90" "[:'x=42]`
Hence, x=42 and y=48
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