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Lines And Angles

Question
CBSEENMA9002420
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In figure, if QT ⊥ PR, ∠TQR = 40° and ∠SPR = 30°, find the value of x and y.

Solution

In ∆QTR,
∠QTR + ∠r + 40° = 180°
| ∠ Angle sum property of a triangle
⇒ 90° + ∠x + 40° = 180°
⇒    ∠r + 130° = 180°
⇒ ∠x = 180° - 130° = 50°
∠x = 50°
In ∠PSR,
y° = x° + 30°
| Exterior angle theorem
= 50° + 30°
= 80°
⇒    y = 80°

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.

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