Q. 44.3( 21 Votes )

In the figure, QT

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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