Chapter 5.2, Problem 56SR

To determine

To prove: The $m\angle X+m\angle Z=m\angle 1$ by using Exterior Angle Theorem.

Answer to Problem 56SR

It is proved that $m\angle X+m\angle Z=m\angle 1$ .

Explanation of Solution

Given:

The given diagram is as follows.

  

Calculation:

Angles that form a straight angle are supplementary which means $\angle 1$ and $\angle 2$ are supplementary.

By the definition of supplementary,

  $m\angle 1+m\angle 2=180$

By the Triangle Angle - Sum Theorem,

  $m\angle X+m\angle Y+m\angle Z=180$

By Substitution Property,

  $\begin{array}{c}m\angle 1+m\angle 2=m\angle X+m\angle Y+m\angle Z\\ m\angle 1=m\angle X+m\angle Y\end{array}$