#### Answer

x = 2$^{\circ}$
So angles are:
$\frac{80}{x}$ = $\frac{80}{2}$ = 40$^{\circ}$
$\frac{100}{x}$ = $\frac{100}{2}$ = 50$^{\circ}$

#### Work Step by Step

Given, that $\frac{80}{x}$ and $\frac{100}{x}$ are complementary angles.
Thus, $\frac{80}{x}$ + $\frac{100}{x}$ = 90$^{\circ}$
Since denominators are same (x), thus we can directly add the numerators ( 80 and 100)
Thus, $\frac{80}{x}$ + $\frac{100}{x}$ = $\frac{180}{x}$
Since $\frac{180}{x}$ = 90$^{\circ}$
thus x = $\frac{180}{90}$$^{\circ}$ = 2$^{\circ}$
So angles are:
$\frac{80}{x}$ = $\frac{80}{2}$ = 40$^{\circ}$
$\frac{100}{x}$ = $\frac{100}{2}$ = 50$^{\circ}$