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°
Rate this question :






















In a triangle ABC, ∠B = 70°. Find ∠A + ∠C.
Karnataka Board - Mathematics Part IIn a triangle ABC, ∠A = 110° and AB = AC. Find ∠B and ∠C.
Karnataka Board - Mathematics Part IIn right angled triangle, ∠A is right angle and ∠B = 35°, then ∠C is _______
Karnataka Board - Mathematics Part IIn a triangle ABC, ∠A = 80° and AB = AC, then ∠B is ______
Karnataka Board - Mathematics Part IIn the figure, QT ⊥ PR, ∠TQR = 40° and ∠SPR = 30°. Find ∠TRS and ∠PSQ.
In a triangle ABC, if 2∠A = 3∠B = 6∠C, determine ∠a, ∠B and ∠C.
Karnataka Board - Mathematics Part IIf three angles of a triangle are in the ratio 2:3:5, determine three angles.
Karnataka Board - Mathematics Part IThe angles of a triangle are x – 40°, x – 20° and x + 15°. Find the value of x.
Karnataka Board - Mathematics Part I