Answer
\begin{array}{c|ll}& \textbf{Statement} & \textbf{Reasons}
\\\hline1 & \angle1\cong\angle2 & \text{Given}
\\2 & \angle1\cong\angle3 & \text{Vertical Angles are Congruent}
\\3 & \angle2\cong\angle3 & \text{Transitive Property of Congruence}
\\4 & \angle2\cong\angle4 & \text{Vertical Angles are Congruent}
\\5 & \angle1\cong\angle2\cong\angle3\cong\angle4 & \text{Transitive Property of Congruence}
\end{array}
Work Step by Step
You could also use the definition of a linear pair to prove all the angles are congruent. $\angle1$ and $\angle2$ are a linear pair and are congruent, so must measure 90. You can use the definition of a linear pair to prove that all 4 angles have a measure of 90, so all are congruent.
