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Lines and Angles
Question
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In figure, if AB || DE, ∠BAC = 35° and ∠CDE = 53°, find ∠DCE.

Answer

∠DEC = ∠BAC = 35°    ...(1)
| Alternate Interior Angles
∠CDE = 53°    ...(2) | Given
In ∆CDE,
∠CDE + ∠DEC + ∠DCE = 180°
| ∵ The sum of all the angles of a triangle is 180°.
⇒ 53°+ 35° + ∠DCE = 180°
| Using (1) and (2)
⇒    88° + ∠DCE = 180°
⇒    ∠DCE = 180° - 88° = 92°.

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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.