Banner 0
Banner 1
Banner 2
Banner 3
Banner 4
Banner 5
Banner 6
Banner 7
Banner 8
Banner 9

Q.

PQRS is a trapezium as shown in the figure with PQ ∥ RS, then what is the difference between ∠S and ∠R?

Question Image

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

a

20°

b

25°

c

50°

d

75°

answer is B.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

JEE

NEET

NEET

Foundation JEE

Foundation JEE

Foundation NEET

Foundation NEET

CBSE

CBSE

Detailed Solution

Given: PQ ∥ RS
∠Q = 90°
∠P = 115°
PQ ∥ RS, QR acts as a transversal. Also, ∠Q and ∠R are co-interior angles.
⇒ ∠Q + ∠R = 180° (∵ Sum of co-interior angles is 180°)
⇒ 90° + ∠R = 180°
⇒ ∠R = 90°
In trapezium PQRS, 
⇒ ∠P + ∠Q + ∠R + ∠S = 360° (∵ Sum of all angles of a quadrilateral is 360°)
⇒ 115° + 90° + 90° + ∠S = 360°

⇒ ∠S = 360° - 295°
⇒ ∠S = 65°
Now, ∠R − ∠S = 90° − 65° = 25°
Thus, the difference between ∠R and ∠S is 25°.

Watch 3-min video & get full concept clarity
score_test_img

courses

No courses found

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!

best study material, now at your finger tips!

  • promsvg

    live classes

  • promsvg

    progress tracking

  • promsvg

    24x7 mentored guidance

  • promsvg

    study plan analysis

download the app

gplay
mentor

Download the App

gplay
whats app icon
personalised 1:1 online tutoring