In Fig. 6. 16, ifx + y = w + z, then prove that AOBis a line.

1.	In Fig. 6. 16, ifx + y = w + z, then prove that AOBis a line.
Answer» 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.

Answer»

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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