Q. 44.3( 21 Votes )
In the figure, QT ⊥ PR, ∠TQR = 40° and ∠SPR = 30°. Find ∠TRS and ∠PSQ.
Answer :
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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