## Algebra: A Combined Approach (4th Edition)

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