Question

4. In Fig. 6.16, if x + y = w+ , then prove that AOB
Fig. 6.15
is a line
12​

Answer 1

Answer:

Solution: 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.

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.

Plz mrk as brainliest ❤