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Lines and Angles
Question
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In figure, if line segment AB intersects CD at O such that ∠OAD = 80°, ∠ODA = 50° and ∠OCB = 40°, then find ∠OBC.

Answer

In ∆OAD,
∠OAD + ∠ODA + ∠AOD = 180°
| Angle sum property of a triangle
⇒ 80° + 50° + ∠AOD = 180°
⇒    130° + ∠AOD = 180°
⇒ ∠AOD = 180° - 130° = 50°
⇒ ∠BOC = 50°
| ∵ ∠AOD = ∠BOC (Vertically opposite angles)
In ∆OBC,
∠BOC + ∠OCB + ∠OBC = 180°
| Angle sum property of a triangle ⇒ 50° + 40° + ∠OBC = 180°
⇒     90° + ∠OBC = 180°
∠    ∠OBC = 180° - 90° = 90°

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Some More Questions From Lines and Angles Chapter

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.

In figure, if ∠POR and ∠QOR form a linear pair and a - b = 80° then find the value of a and b.