Q. 73.6( 11 Votes )

In Fig. 6.3, if O

Answer :

In the figure, it is given to us that –


OP || RS


OPQ = 110°


QRS = 130°


We have to find PQR.


Let us extend OP, so as to intersect QR at point D. The figure is as -


Now, we have OP || RS and, DR is a transversal.


We know, if a transversal intersects two parallel lines, then each pair of alternate angles are equal.


DRS = RDP


It is given to us that QRS = 130°


DRS = 130°


RDP = 130° - - - - (i)


Now, we have QR as a line segment. By linear pair axiom,


PDQ + PDR = 180°


QDP + RDP = 180°


QDP = 180° - RDP


QDP = 180° - 130°


QDP = 50°


PDQ = 50° - - - - (ii)


In ΔPQD,


OPQ is an exterior angle.


Also, we know that exterior angle is equal to the sum of the two interior opposite angles.


OPQ = PQD + PDQ - - - - (iii)


We have OPQ = 110° and from equation (ii) we have PDQ = 50°.


So, equation (iii) can be written as –


110° = PQD + 50°


PQD = 60°


So, PQR = 60°


Thus, option (C) is correct.


Option (A) is not correct. If PQR is equal to 40°, then it won’t satisfy the linear axiom. So, PQR is not 40°.


Option (B) is not correct. We have got PDQ = 50°. If PQR = 50°, then the exterior angle, i.e., OPQ = 110° is not equal to the sum of the opposite interior angles, PDQ and PQR which are now 50° each. So, PQR is not equal to 50°.


Option (D) is not correct. We have, OPQ = 110°. By linear pair axiom, QPD = 70°. So, PQR is not equal to 700

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Introduction to Lines and AnglesIntroduction to Lines and AnglesIntroduction to Lines and Angles60 mins
Bonus Questions - 1Bonus Questions - 1Bonus Questions - 156 mins
Revision on Angle sum Property of TrianglesRevision on Angle sum Property of TrianglesRevision on Angle sum Property of Triangles44 mins
Bonus Questions - 2Bonus Questions - 2Bonus Questions - 257 mins
Parallel Lines and Transversal LinesParallel Lines and Transversal LinesParallel Lines and Transversal Lines22 mins
Pair of AnglesPair of AnglesPair of Angles29 mins
Elections- Mechanism and TypesElections- Mechanism and TypesElections- Mechanism and Types48 mins
Constitution - Formation and ObjectiveConstitution - Formation and ObjectiveConstitution - Formation and Objective63 mins
Kinetic and Potential EnergyKinetic and Potential EnergyKinetic and Potential Energy39 mins
Construction-2Construction-2Construction-244 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

The sides BC, BA RS Aggarwal & V Aggarwal - Mathematics

In the given figuRS Aggarwal & V Aggarwal - Mathematics

In the given figuRS Aggarwal & V Aggarwal - Mathematics

The angles of a tRS Aggarwal & V Aggarwal - Mathematics

In ΔABC, <span laRS Aggarwal & V Aggarwal - Mathematics

In ΔABC, BD <spanRS Aggarwal & V Aggarwal - Mathematics

In the given figuRS Aggarwal & V Aggarwal - Mathematics

In a ΔABC its is RS Aggarwal & V Aggarwal - Mathematics

Side BC of ΔABC hRS Aggarwal & V Aggarwal - Mathematics

An exterior angleRS Aggarwal & V Aggarwal - Mathematics