Consider that if x is the smaller angle and y is the grater angle, you can write:
[tex]\frac{x}{y}=\frac{7}{8}[/tex]the two angles are complementary, then, you can write:
[tex]x+y=90[/tex]In order to determine the values of x, proceed as follow:
Solve for y from the first equation:
[tex]\begin{gathered} \frac{x}{y}=\frac{7}{8} \\ y=\frac{8}{7}x \end{gathered}[/tex]Next, replace the previous expression into the second equation and solve for x:
[tex]\begin{gathered} x+y=90 \\ x+\frac{8}{7}x=90 \\ \frac{15}{7}x=90 \\ x=\frac{90}{15}\cdot7=42 \end{gathered}[/tex]Hence, the smaller angle is 42 degrees
