The angles ∠GHI and ∠JKL are complementary, this means that they add up to 90°
Then we can say that
[tex]\angle\text{GHI}+\angle\text{JKL}=90^{\circ}[/tex]For
∠GHI= (5x+6)°
∠JKL= (3x+4)°
[tex](5x+6)+(3x+4)=90[/tex]From this expression you can calculate the value of x
First step is to order the like terms together and simplify them}
[tex]\begin{gathered} 5x+3x+6+4=90 \\ 8x+10=90 \\ 8x=90-10 \\ 8x=80 \end{gathered}[/tex]Next divide both sides of the equation by 8 to reach the value of x
[tex]\begin{gathered} \frac{8x}{8}=\frac{80}{8} \\ x=10 \end{gathered}[/tex]Now that we knoe the value of x, we can calculate the measure of both angles
[tex]\begin{gathered} \angle\text{GHI}=5x+6 \\ \angle\text{GHI}=5\cdot10+6 \\ \angle\text{GHI}=56 \end{gathered}[/tex][tex]\begin{gathered} \angle\text{JKL}=3x+4 \\ \angle\text{JKL}=3\cdot10+4 \\ \angle\text{JKL}=34 \end{gathered}[/tex]