We have the measure of angles 1 and angle 2, as we can see from the diagram in the image, angles 1 and 2 added form the right angle (90°) in the figure.
Thus, the sum of x-6 and 5x, must be equal to 90°.
(a) Write an equation:
[tex]x-6+5x=90[/tex]
(b) To find the degree measure of each angle, first we need to solve for the value of x in the equation.
Combining like terms:
[tex]6x-6=90[/tex]
Adding 6 from both sides:
[tex]\begin{gathered} 6x-6+6=90+6 \\ 6x=96 \\ \end{gathered}[/tex]
Divide both sides by 6:
[tex]\begin{gathered} \frac{6x}{6}=\frac{96}{6} \\ x=16 \end{gathered}[/tex]
Now that we have x, we find angle 1:
[tex]m\angle1=x-6=16-6=10[/tex]
And the measure of angle 2:
[tex]m\angle2=5x=5(16)=80[/tex]
