# Chapter 2 - Reasoning and Proof - Common Core Cumulative Standards Review - Selected Response - Page 136: 23

\begin{array}{c|ll}& \textbf{Statement} & \textbf{Reasons} \\\hline1 & \angle1\text{ and }\angle2\text{ are supplementary} & \text{Given} \\2 & m\angle1+m\angle2=180 & \text{Definition of Supplementary} \\3 & \angle1\cong\angle2 & \text{Vertical Angles Theorem} \\4 & m\angle1=m\angle2 & \text{Definition of Congruency} \\5 & m\angle1+m\angle1=180 & \text{Substitution} \\6 & 2m\angle1=180 & \text{Combine Like Terms} \\7 & m\angle1=90 & \text{Division Property of Equality} \\8 & m\angle2=90 & \text{Substitution} \\9 & \angle1\text{ and }\angle2\text{ are right angles} & \text{Definition of Right Angle} \end{array}

#### Work Step by Step

Use the given information, known definitions, postulates, and proven theorems to write a proof.

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