91Ó°ÊÓ

The given diagram is:

As∠3 is supplementary to∠1 , therefore the sum of the angles∠3 and∠1 is 180°.

Therefore, the relation between the angles∠3 and∠1 is that the sum of the angles∠3 and∠1 is 180°.

That implies, $m∠3+m∠1=180°\left(1\right)$.

As ∠4 is supplementary to ∠2, therefore the sum of the angles ∠4 and ∠2 is 180°.

Therefore, the relation between angles ∠4 and ∠2 is that the sum of angles ∠4 and ∠2 is 180°.

That implies, $m∠4+m∠2=180°\left(2\right)$.

From the given diagram it can be noticed that angles ∠1 and ∠2 are the vertical angles.

Therefore, by using the theorem of vertical angles it can be said that angles ∠1 and ∠2 are congruent angles.

That implies, $m∠1=m∠2$.

From the equations (1) and (2), it is obtained that:

$$\begin{gathered} m∠3+m∠1=m∠4+m∠2 \\ m∠3+m∠2=m∠4+m∠2\left(âˆ\mu m∠1=m∠2\right) \\ m∠3=m∠4 \end{gathered}$$

Therefore, the relation between angles ∠3 and ∠4 is $m∠3=m∠4$.

That implies $∠3â‰\dots ∠4$.

The two-column proof is: