Chapter 3, Problem 17SGR

To determine

To Find: Themeasure of the given angle and determine the postulates or theorem you used.

Answer to Problem 17SGR

The value of $m\angle 11=123$ by the definition of the congruence.

Explanation of Solution

Given:

The given diagram is shown in Figure 1

  

Figure 1

The given angles is $\angle 11$ ,

The angle $m\angle 1=123$ .

Calculation:

It is given that $m\angle 1=123$ as $p\left|\right|q$ and by the corresponding angles formed and by the pair of the parallel line and the congruent transversal $\angle 1\cong \angle 3$ . Then, the angle $m\angle 3$ is,

  $\begin{array}{l}m\angle 3=m\angle 3\\ m\angle 3=123\end{array}$

Consider that $r\left|\right|s$ as $\angle 1\cong \angle 11$ since the angle formed by the pair of the parallel lines and the transversal is congruent. Then by the definition of the congruence,

  $m\angle 11=123$