Question

Fig. 6.15
4. In Fig. 6.16, if x + y =w+z, then prove that AOB
is a line.
B
Fig. 6.16​

Answer 1

Answer:

Step-by-step explanation:

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:

According to the question,

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

Question :-

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

Answer :-

Sum of all the angles at a point = 360°

∴ x + y + z + w = 360° or, (x + y) + (z + w) = 360°

But (x + y) = (z + w) [Given]

∴ (x + y) + (x + y) = 360° or,

2(x + y) = 360°

or, (x + y) = 360° /2 = 180°

∴ AOB is a straight line.

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