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Lines and Angles
Question
Wired Faculty App

In figure, ∠PQR = ∠PRQ, then prove that ∠PQS = ∠PRT.

Answer

∵ Ray QP stands on line ST
∴ ∠PQS + ∠PQR = 180°    ...(1)
| Linear Pair Axiom
∵ Ray RP stands on line ST
∴ ∠PRQ + ∠PRT = 180°    ...(2)
| Linear Pair Axiom
From (1) and (2), we obtain
∠PQS + ∠PQR = ∠PRQ + ∠PRT
⇒    ∠PQS = ∠PRT.
| ∵ ∠PQR = ∠PRQ (Given)

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Some More Questions From Lines and Angles Chapter

Ray OE bisects ∠AOB and OF is the ray opposite to OE. Show that ∠FOB = ∠FOA.

Rays OA, OB. OC, OD and OE have the common initial point O. Show that ∠AOB + ∠BOC + ∠COD + ∠DOE + ∠EOA = 360°.

Prove “if two lines intersect each other, then the vertically opposite angles are equal.”

In figure, OP bisects ∠AOC, OQ bisects ∠BOC and OP ⊥ OQ. Show that the points A, O and B are collinear.

In figure, if y = 20°, prove that the line AOB is a straight line.

In the given figure, lines AB and CD intersect at O. If ∠AOC + ∠BOE = 70° and ∠BOD = 40°, find ∠BOE and reflex angle EOC.

In figure, lines PQ and RS intersect each other at point O. If ∠POR : ∠ROQ = 5 : 7, find all the angles. 

In figure, ray OS stands on a line POQ. Ray OR and ray OT are angle bisectors of ∠POS and ∠SOQ, respectively. If ∠POS = x, find ∠ROT.

If the complement of an angle is one-third of its supplement, find the angle. 

In figure, find the value of x.