Question

If x+y=w+z, then prove that AOB is a line.​

Answer 1

Answer:

Given-x+y=w+z

To prove -AOB is a line

Proof-x+y+w+z=360

x+y+x+y=360[x+y=w+z]

2x+2y=360

2(x+y)=360

x+y=180

AOB is a line

Answer 2

Solution:

For proving AOB is a straight line, we will have to prove x+y is a linear pair

i.e. x+y = 180°

We know that the angles around a point are 360° so,

x+y+w+z = 360°

In the question, it is given that,

x+y = w+z

So, (x+y)+(x+y) = 360°

2(x+y) = 360°

∴ (x+y) = 180° (Hence proved).