Chapter 7.2, Problem 69SPR

To determine

To find: The measure of the numbered angle.

Answer to Problem 69SPR

The value of $m\angle 3=68°$ .

Explanation of Solution

Given:

The given diagram is shown in Figure 1

  

Figure 1

The numbered angle is $m\angle 3$ .

Calculation:

Consider that in the given figure the measure of the interior angle is equal to the sum of the measure of the two remote interior angles this is exterior angle theorem.

Consider the angle relation as,

  $\begin{array}{c}m\angle 1=m\angle A+m\angle C\\ =50+78\\ =128\end{array}$

Consider the supplementary angle relationship as,

  $\begin{array}{l}m\angle 1+m\angle 2=180\\ 128+m\angle 2=180\\ m\angle 2=180-128\\ m\angle 2=52\end{array}$

Consider the triangle $\Delta DFG$ as,

  $\begin{array}{l}m\angle 2+m\angle 3=m\angle FGE\\ 52+m\angle 3=120\\ m\angle 3=68\end{array}$

Thus, the value of

  $m\angle 3=68°$ .