Question

in the figure if x+y=w+z then prove that aob is a line

Answer 1

hey mate ,

   here is your answer :)

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Linear pair of angles:

If Non common arms of two adjacent angles form

a line, then these angles are called linear pair of angles.

 

Axiom- 1

If a ray stands on a line, then the sum of two

adjacent angles so formed is 180°i.e, the sum of the linear pair is 180°.

 

Axiom-2

If the sum of two adjacent angles is 180° then

the two non common arms of the angles form a line.

 

The two axioms given above together are called

the linear pair axioms.

 

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Solution:

 

Given,

x + y = w + z

To Prove,

AOB is a line or

x + y = 180° (linear pair.)

Proof:

A.T.Q

x + y + w + z = 360° (Angles around a point.)

(x + y) +  (w + z) = 360°

(x + y) +  (x + y) = 360°

(Given x + y = w + z)

2(x + y) = 360°

(x + y) = 180°

Hence, x + y makes a linear pair.

Therefore, AOB is a straight line.

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Hope this will help you....

Answer 2

hi mate here is your answer ..

x+y=w+z

x+y=w+z = 360

x+y+x+y = 360

2x+2y = 360

2(x+y) = 360

x+y = 360/2

x+ y = 180

so therefore aob is a line ....

hope it is useful.... if so mark this as brainliest answer...