91Ó°ÊÓ

The given diagram is:

As $∠2â‰\dots ∠3$that implies angles ∠2 and ∠3 are congruent angles.

The congruent angles are the angles that have the same measure.

Therefore, the relation between angles ∠2 and ∠3 is that angles ∠2 and ∠3 have the same measure.

That implies, $m∠2=m∠3$.

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 given diagram it can be noticed that angles ∠3 and ∠4 are the vertical angles.

Therefore, by using the theorem of vertical angles it can be said that angles ∠3 and ∠4 are congruent angles.

That implies, $m∠3=m∠4$.

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

Therefore, the relation between the angles∠1 and∠4 is .

That implies $∠1â‰\dots ∠4$.

The two column proof is: