Chapter 1.5, Problem 7PSA

To determine

To Evaluate : The value of $m\left(\angle FGJ\right)$

Answer to Problem 7PSA

  $m\left(\angle FGJ\right)=43°$

Explanation of Solution

Given information :

  $\begin{array}{l}m\left(\angle FGJ\right)=3x-5\\ m\left(\angle JGH\right)=x+27\\ \overrightarrow{GJ}\text{ bisects }\angle FGH.\end{array}$

  

Concept Used:

Bisector bisect the angle in two equal parts of equal measure.

Calculation:

Here, we have

  $\begin{array}{l}m\left(\angle FGJ\right)=3x-5\\ m\left(\angle JGH\right)=x+27\\ \overrightarrow{GJ}\text{ bisects }\angle FGH.\\ \Rightarrow m\left(\angle FGJ\right)=m\left(\angle JGH\right)\\ \Rightarrow 3x-5=x+27\\ \Rightarrow 2x=32\\ \Rightarrow x=16\\ \therefore m\left(\angle FGJ\right)=3\times 16-5=43\\ m\left(\angle JGH\right)=16+27=43\end{array}$

  $\text{Hence, }m\left(\angle FGJ\right)=43°$