91Ó°ÊÓ

The given diagram is:

It is being given that$m∠DBA=45$ and $m∠DEB=45$.

From the diagram it can be noticed that the angles$∠DBA$ and$∠DBC$ forms the linear pair.

Therefore, the sum of the angles$∠DBA$ and$∠DBC$ is $180$.

That implies, $∠DBA+∠DBC=180$.

Therefore, it can be obtained that:

$$\begin{gathered} ∠DBA+∠DBC=180 \\ 45+∠DBC=180 \\ ∠DBC=180−45 \\ ∠DBC=135 \end{gathered}$$

Therefore, the measure of the angle$∠DBC$ is 135.

From the diagram, it can be noticed that the angles$∠DEB$ and$∠FEB$ forms the linear pair.

Therefore, the sum of the angles$∠DEB$ and$∠FEB$ is 180.

That implies, $∠DEB+∠FEB=180$.

Therefore, it can be obtained that:

$$\begin{gathered} ∠DEB+∠FEB=180 \\ 45+∠FEB=180 \\ ∠FEB=180−45 \\ ∠FEB=135 \end{gathered}$$

Therefore, the measure of the angle$∠FEB$ is 135.

As, $∠DBC=∠FEB=135$, therefore $∠DBCâ‰\dots ∠FEB$.

Hence proved.

The two column proof is: