Chapter 3, Problem 15SGR

To determine

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

Answer to Problem 15SGR

The value of $m\angle 14=57$ by the supplementary angles theorem.

Explanation of Solution

Given:

The given diagram is shown in Figure 1

  

Figure 1

The given angles is $\angle 14$ ,

The angle $m\angle 1=123$ .

Calculation:

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

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

The $r\left|\right|s$ then, by then $\angle 1\cong \angle 11$ by the pair of parallel lines and transversal are congruent $\angle 1\cong \angle 3$ . Then, by the definition of the congruence,

  $\begin{array}{l}m\angle 11=m\angle 3\\ m\angle 11=m\angle 123\end{array}$

Consider that $\angle 11=\angle 14$ are supplementary as they form the line linear pair then supplementary angle theorem the value of $m\angle 14$ is,

  $\begin{array}{l}m\angle 14=180-m\angle 11\\ m\angle 14=180-123\\ m\angle 14=57\end{array}$

Then, the value of $m\angle 14=57$ by the supplementary angles theorem.