Given,
The measure of one of the angle is 65 degree.
From the diagram,
It is clear that a transversal is passing through the pair of parallellines.
The sum of adjacent angles between two parallel line is 180 degree.
So,
[tex]\begin{gathered} 65^{\circ}+\angle6=180^{\circ} \\ \angle6=180^{\circ}-65^{\circ} \\ \angle6=115^{\circ}^{} \end{gathered}[/tex]
The angle 6 and angle 5 are vertical opposite equal angles.
[tex]\begin{gathered} \angle6=\angle5\text{ (vertical opposite angle)} \\ \angle5=115^{\circ} \end{gathered}[/tex]
Hence, the measure of angle 5 is 115 degree.
