Question

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

Answer 1

Given: ∠SPR = 30°, ∠TQR = 40° and QT ⊥ PR i.e., ∠QTR = 90°

To Find: ∠TRS and ∠PSQ

Solution:

In ΔQTR, ∠QTR + ∠TQR + ∠TRQ = 180° (Sum of the angles of a triangle)

90° + 40° + ∠TRQ = 180°

∠TRQ = 180° − 130°

∠TRQ = 50°

∴∠TRS = 50°

In ΔPSR, ∠SPR + ∠PRS + ∠RSP = 180° (Sum of the angles of a triangle)

30° + 50° + ∠RSP = 180°

∠RSP = 180° − 80°

∠RSP = 100°

∠RSP + ∠PSQ = 180° (Linear angles)

100° + ∠PSQ = 180°

∠PSQ = 180° − 100°

∴∠PSQ = 80°