Chapter 3, Problem 16SGR

To determine

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

Answer to Problem 16SGR

The value of $m\angle 16=57$ by the supplementary angles theorem.

Explanation of Solution

Given:

The given diagram is shown in Figure 1

  

Figure 1

The given angles is $\angle 16$ ,

The angle $m\angle 1=123$ .

Calculation:

The $r\left|\right|s$ then, by then $\angle 1\cong \angle 9$ as the corresponding angle formed by the pair of parallel lines and transversal are congruent. Then, by the definition of the congruence,

  $\begin{array}{l}m\angle 9=m\angle 1\\ m\angle 9=m\angle 123\end{array}$

Consider that $\angle 9$ and $\angle 16$ are supplementary as they form the line linear pair then supplementary angle theorem the value of $m\angle 16$ is,

  $\begin{array}{l}m\angle 16=180-m\angle 9\\ m\angle 16=180-123\\ m\angle 16=57\end{array}$

Then, the value of $m\angle 16=57$ by the supplementary angles theorem.