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Question
PQRS is a rectangle. The perpendicular ST from S on PR divides ∠S in the ratio 2:3. Find ∠TPQ.
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Solution
Given, ST ⊥ PR and ST divides ∠S in the ratio 2:3
So, sum of ratio = 2 + 3 = 5
Now, `∠TSP = 2/5 xx 90^circ = 36^circ, ∠TSR = 3/5 xx 90^circ = 54^circ`
Also, by the angle sum property of a triangle,
∠TPS = 180° – (∠STP + ∠TSP)
= 180° – (90° + 36°)
= 54°
We know that, ∠SPQ = 90°
⇒ ∠TPS + ∠TPQ = 90°
⇒ 54° + ∠TPQ = 90°
⇒ ∠TPQ = 90° – 54° = 36°
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