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Lines and Angles
Question
Wired Faculty App

In figure, AB || CD and CD || EF. Also EA ⊥ AB. If ∠BEF = 40°, then find x, y, z.

Answer

∵ CD || EF and a transversal DE intersects them
∴ y + 40° = 180°
| Sum of consecutive interior on the same side of a transversal is 180°
⇒ y = 180° - 40° = 140°
∵ AB || CD and a transversal BD intersects them
x = y    | Corresponding angles
⇒ x = 140°
∵ EA ⊥ AB and AB || EF
∵ EA ⊥ EF
| If a line is perpendicular to a line, then it is perpendicular to the parallel line also
⇒ ∠AEF = 90°
⇒ z + 40° = 90°
⇒    z = 50°

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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.