Chapter 4, Problem 8CUR

To determine

Find $m\angle G$ .

Answer to Problem 8CUR

  $m\angle G=86$

Explanation of Solution

Given:

In quadrilateral EFGH , $\overline{EF}\parallel \overline{HG}$ , $m\angle E=y+10$ , $m\angle F=2y-40$ , and $m\angle H=2y-31$ .

Calculation:

Since , $\overline{EF}\parallel \overline{HG}$ in a quadrilateral, so ,

  $\begin{array}{l}m\angle E+m\angle H=180\\ \Rightarrow y+10+2y-31=180\\ \Rightarrow 3y-21=180\\ \Rightarrow 3y=180+\mathrm{21................}[\text{add 21 each side]}\\ \Rightarrow y=\frac{201}{3}\mathrm{........................}[\text{divide each side by 3]}\\ \Rightarrow y=67\end{array}$

  $\begin{array}{l}m\angle F+m\angle G=180\\ \Rightarrow 2y-40+m\angle G=180\\ \Rightarrow 2(67)-40+m\angle G=\mathrm{180....}[y=67]\\ \Rightarrow 94+m\angle G=180\\ \Rightarrow m\angle G=180-\mathrm{94..............}[\text{subtract 94 from each side]}\\ \Rightarrow m\angle G=86\end{array}$