Question

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

Answer 1

Answer ⤵️

Answer: Given: (x + y) = (w + z)

To prove: ∠AOB

Proof: As, Sum of all angles in a circle is always 360°

So, according to the question, we get:

∠AOC + ∠BOC + ∠DOB + ∠AOD = 360°

=> x + y + w + z = 360°

=> x + y + x + y = 360°

(given = (x+y = w+z) so we can use x+y in the place of w+z because they are equal to each other as given)

Adding the value we get,

=> 2x + 2y = 360°

= 360°=> 2(x + y) = 360°

=> x + y = 360°/2

=> x + y = 180° (linear pair)

or ∠AOC + ∠BOC = 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 ❤