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Lines And Angles

Question

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In figure, if AB II CD, ∠APQ = 50° and ∠PRD = 127°, find x and y.

Solution

x = ∠APQ = 50°
| Alternate Interior Angles
∠APQ + y = ∠PRD = 127°
| Alternate Interior Angles
50° + y = 127°
y = 127° - 50° = 77°

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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