SOLUTION
Solve for the value of x using supplementary angles
If the sum of two angles is 180 degrees then they are said to be supplementary angles, which form a linear angle together.
[tex]\begin{gathered} <1=4x-5 \\ <2=x \end{gathered}[/tex]
To solve using the supplementary angle rule
Add the two angles together
[tex]\begin{gathered} <1+<2=180^0 \\ 4x-5+x=180 \\ collect\text{ like terms} \\ 4x+x=180+5 \\ 5x=185 \end{gathered}[/tex]
Divide both side by 5
[tex]\begin{gathered} 5x=185 \\ \frac{5x}{5}=\frac{185}{5} \\ x=37 \end{gathered}[/tex]
Hence the value of x = 37 degree
The measure of Angle 1 = <1 = 4x-5 = 4(37) - 5 = 143 degree
The measure of Angle 2 = <2 = x = 37 degree
