We have the parallel lines:
Angles c and b are vertical angles, and the same is true for a and 54°. The definition of two vertical angles is that they are equal. Then:
[tex]\begin{gathered} a=54^{\circ} \\ c=b \end{gathered}[/tex]
Additionally, c and a are consecutive exterior angles, which are equal by definition. We conclude that:
[tex]\begin{gathered} c=a\Rightarrow c=54^{\circ} \\ \Rightarrow b=54^{\circ} \end{gathered}[/tex]
