In the figure QT ⊥ PR, ∠TOR = 40° and ∠SPR = 30° find ∠TRS a – InterviewSolution

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1.

In the figure QT ⊥ PR, ∠TOR = 40° and ∠SPR = 30° find ∠TRS and ∠PSQ.

Answer»

In ΔTQR,

∠TQR + ∠QTR + ∠TRQ = 180°

40° + 90° + ∠TRQ = 180°

130° + ∠TRQ = 180°

∠ TRQ = 180° – 130°

∠ TRQ = 50°

∠ TRS = 50°

[∠PRS is same as ∠TRS ]

In Δ PRS,

RS is produced to Q

∴Exterior∠PSQ = ∠SPR + ∠PRS

= 30° + 50°

∠PSQ = 80°

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