Question

pqrs is a rectangle the perpendicular of ST from s on PR divide Angle angle s in the ratio 2 ratio 3 find TPS​

Answer 1

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Step-by-step explanation:

Given, 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° = ∠RPQ = ∠ PRS = QSR,

∠TSR = 54° = ∠SPT

Hence , ∠TPQ = ∠SPQ – ∠TPS = 90° – 54° = 36°.

Hope it will help you.