Question

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

Answer 1

Step-by-step explanation:

s Given, x+y=w+z

To Prove: AOB is a line or x+y=180

∘

(linear pair.)

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.

Answer 2

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Sum of all angles in a circle always 360°

Hence

∠AOC + ∠BOC + ∠DOB + ∠AOD = 360°

=> x + y + w + z = 360°

=> x + y + x + y = 360°

Given that x + y = w + z

Plug the value we get

=> 2w + 2z = 360°

=> 2(w + z) = 360°

w + z = 180° (linear pair)

or ∠BOD + ∠AOD = 180°

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

Hence AOB is a line.