Chapter 3, Problem 18SGR

To determine

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

Answer to Problem 18SGR

The value of $m\angle 4=57$ by the supplementary angles theorem.

Explanation of Solution

Given:

The given diagram is shown in Figure 1

  

Figure 1

The given angles is $\angle 4$ ,

The angle $m\angle 1=123$ .

Calculation:

Since, $m\angle 1=123$ and $p\left|\right|q$ then, as the corresponding angle formed by angle formed by the pair of parallel lines and transversal are congruent $\angle 1\cong \angle 3$ . The exterior angles theorem.

  $\begin{array}{l}m\angle 3=m\angle 1\\ m\angle 3=m\angle 123\end{array}$

Consider that $\angle 3$ and $\angle 4$ are supplementary as they form the line linear pair then supplementary angle theorem the value of $m\angle 14$ is,

  $\begin{array}{l}m\angle 4=180-m\angle 3\\ m\angle 4=180-123\\ m\angle 4=57\end{array}$

Then, the value of $m\angle 4=57$ by the supplementary angles theorem.