Q136 of 160 Page 144

PQRS is a rectangle. The perpendicular ST from S on PR divides S in the ratio 2:3. Find TPQ.

The figure is given below:


PQRS is a rectangle. The perpendicular ST from S on PR divides angle S in the ratio 2:3.


∠PSR = 90


⟹ It is given that, the perpendicular ST from S on PR divides angle S in the ratio 2:3.


⟹ divide the 90° angle into the ratio 2:3.


2x + 3x = 90


5x = 90


x = 18


⟹ therefore, 2x = 2×18 = 36 and 3x = 3×18 = 54


now, ∠PST = 36 and


∠TSR = 54 = ∠TSQ + ∠QSR


∠PST = 36


∠TSR = 54 = ∠TPS


Hence, ∠TPQ = ∠SPQ-∠TPS = 90-54 = 36


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