In figure, if x + y = w + z, then prove that AOB is a line.

Solution

x + y = w + z ...(1) | Given
∵ The sum of all the angles round a point is equal to 360°.
$therefore$ x + y + w + z = 360⁰
$rightwards double arrow$ x + y + x + y = 360⁰ | Using (1)
$rightwards double arrow$ 2(x + y) = 360⁰
$rightwards double arrow space space space space space space space space space space space space space straight x plus straight y equals fraction numerator 360 degree over denominator 2 end fraction$
$rightwards double arrow$ x + y = 180⁰

∴ AOB is a line.

| If the sum of two adjacent angles is 180°, then the non-common arms of the angles form a line.

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°.

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Lines And Angles

In figure, if x + y = w + z, then prove that AOB is a line.

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.

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