Chapter 3.7, Problem 25PSC

To determine

To calculate : The values of x , y and $\angle F$ .

Answer to Problem 25PSC

The final values are $\angle F={60}^0,x=22,y=8$

Explanation of Solution

Given information : The following information has been given

  $\Delta FED$ is equilateral

  $\overrightarrow{GE}\perp \overrightarrow{DE}$

  $m\angle FEG=x+y$

  $m\angle D=3x-6$

  $m\angle F=6y+12$

Formula used : All the sides of an equilateral measure equal to ${60}^0$

Calculation : firstly, we know that all the sides of an equilateral measure equal to ${60}^0$ , thus

  $m\angle F=6y+12={60}^0\to y=8$

  $m\angle D=3x-6={60}^0\to x=22$

And, as all sides of an equilateral measure equal to ${60}^0$ , thus

  $\angle F={60}^0$