Question

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

Answer 1

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°