Question

Can I have help finding each of the missing variables please?

Answer 1

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:

`\begin{gathered} a=54^(\circ) \\ c=b \end{gathered}`

Additionally, c and a are consecutive exterior angles, which are equal by definition. We conclude that:

`\begin{gathered} c=a\Rightarrow c=54^(\circ) \\ \Rightarrow b=54^(\circ) \end{gathered}`