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PQRS is a square and PQT is an equilateral triangle on the side PQ of the square, angle SPT= ----- a)45° b) 40° c) 30° d) 15° |
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Answer» Because PQRS is a square∠PSR=∠QRS=90 ∘ Now In △SRT ∠TSR=∠TRS=60 ∘ ∠PSR+∠TSR=∠QRS+∠TRS⟹∠TSP=∠TRQNow in △TSP and △TRQ TS=TR ∠TSP=∠TRQ PS=QRTherefore , △TSP≡△TRQ So PT=QT (II) Now in △TQR,TR=QR(RQ=SR=TR)∠TQR=∠QTRAnd ∠TQR+∠QTR+∠TRQ=180⟹∠TQR+∠QTR+∠TRS+∠SRQ=180⟹2(∠TQR)+60+90=180 (∠TQR=∠QTR)2(∠TQR)=30⟹∠TQR=15 ∘ |
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