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In fig, if PQ⊥PS,PQ∥SR,∠SQR=280 and ∠QRT=650, then find the value of x and y.
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Given PQ⊥PS,PQ∥SR
∠SQR=28∘,∠QRT=65∘
∠QRS+∠QRT=180∘⟹∠QRS=180∘−65∘=115∘
PQ∥SR⟹∠PQS=∠QSR=x
In △QRS,∠QRS+∠SQR+∠QSR=180∘
⟹x+115∘+28∘=180∘⟹x=37∘
∠PSR=90∘⟹x+y=90∘⟹y=90∘−37∘=63∘
∠SQR=28∘,∠QRT=65∘
∠QRS+∠QRT=180∘⟹∠QRS=180∘−65∘=115∘
PQ∥SR⟹∠PQS=∠QSR=x
In △QRS,∠QRS+∠SQR+∠QSR=180∘
⟹x+115∘+28∘=180∘⟹x=37∘
∠PSR=90∘⟹x+y=90∘⟹y=90∘−37∘=63∘
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