Question

In Fig. if $x+y=w+z$, then prove that $AOB$ is a line.

Answer 1

Prove the given statement

The sum of all angles around a point is ${360}^{\circ }$

Consider the point $O$

The sum of all angles around $O$ must be ${360}^{\circ }$

$\therefore \angle COA+\angle COB+\angle AOD+\angle DOB={360}^{\circ }$

$\therefore$ $x+y+w+z={360}^{\circ }$

$\therefore$ $2(x+y)={360}^{\circ }$ $\left[\because x+y=w+z\right]$

$\therefore$ $x+y={180}^{\circ }$

The sum of angles across $AOB$ is thus ${180}^{\circ }$ thereby making it a straight line

Hence it is proved that $AOB$ is a straight line.