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

Given: TQR = 40° and SPR = 30°.

QTR = 90° (right angle)

As we know, using theorem (1), in any triangle, sum of the three interior angles is 180 °.

So,

TQR + QTR + TRQ = 180°

40° + 90° + TRQ = 180°

TRQ = 180° - 40° - 90°

TRQ = 50°

TRQ = TRS = 50°

Also,

SPR + PRS + RSP = 180°

SPR + TRS + RSP = 180°

30° + 50° + RSP = 180°

RSP = 180° - 30° - 50°

RSP = 100°

As R, S and Q lie on the same line.

So,

RSP + PSQ = 180°

PSQ + 100° = 180°

PSQ = 80°

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