AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

PQRS is a rectangle such that the perpendicular ST from S on PR divides $∠ S$ in the ratio 2:3. Determine $∠ T P Q$ in the ratio 2:3. Determine.

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

36 °

40 °

56 °

64 °

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Given, PQRS is a rectangle such that the perpendicular ST from S on PR divides

∠ S

in the ratio 2:3.
Consider the rectangle PQRS as follows,
Question Image

We have, to determine the angle measure

∠ T P Q

.
So, using the given ratio, we will first find

∠ T S R

.
Now, we know that every interior angle of a rectangle is a right angle.
Then, we can rewrite

∠ S

as a sum of two angles as follows,

∠ P S T + ∠ T S R = 90 ∘

Now, as

∠ S

is divided by ST in the ratio 2:3, so we have,

2 x + 3 x = 90 ∘ 5 x = 90 ∘ x = 90 ∘ 5 x = 18 ∘

So, we have,

∠ T S R = 3 x = 3 × 18 ∘ = 54 ∘

Now, the angle sum property of a triangle says that the sum of all the interior angles of a triangle is always

180 ∘

.
Applying this property on

Δ S R T

and substituting the known angle measures, we get,

∠ T S R + ∠ S T R + ∠ S R T = 180 ∘ 54 ∘ + 90 ∘ + ∠ S R T = 180 ∘ 144 ∘ + ∠ S R T = 180 ∘ ∠ S R T = 180 ∘ − 144 ∘ ∠ S R T = 36 ∘

Now, we know that opposite sides of a rectangle are always parallel to each other.
By this property, we can say that in the rectangle PQRS,

P Q | | R S

and so, the diagonal

P R

acts as a transversal.
Then, by the property of alternate angles, we can say that,

∠ T P Q = ∠ S R T ∠ T P Q = 36 ∘

Hence, the correct option is (1).

Watch 3-min video & get full concept clarity

courses

No courses found

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!