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

Solution:

Given, PQRS is a rectangle.

The perpendicular ST from S on PR divides ∠S in the ratio 2:3.

We have to find the measure of ∠TPQ.

Sum of the ratio = 2 + 3 = 5

∠TSP = (2/5) × 90°

= 180°/5

= 36°

∠TSR = (3/5) × 90°

= 270°/5

= 54°

In triangle PST,

By angle sum property of a triangle,

∠TPS + ∠STP + ∠TSP = 180°

∠TPS + 90° + 36° = 180°

∠TPS + 126° = 180°

∠TPS = 180° - 126°

∠TPS = 54°

We know, ∠SPQ = 90°

∠TPS + ∠TPQ = 90°

54° + ∠TPQ = 90°

∠TPQ = 90° - 54°

∠TPQ = 36°

Therefore, the measure of ∠TPQ = 36°.

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

☛ Also Check: NCERT Solutions for Class 8 Maths

NCERT Exemplar Class 8 Maths Chapter 5 Problem 136

Summary:

PQRS is a rectangle. The perpendicular ST from S on PR divides ∠S in the ratio 2:3. The measure of ∠TPQ is 36 degrees.

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