Answer
x = 6.667$^{\circ}$ or = 6$\frac{2}{3}$$^{\circ}$
Thus,
$\frac{450}{x}$ = 67.5$^{\circ}$
and,
$\frac{150}{x}$ = 22.5$^{\circ}$
Work Step by Step
Given, that $\frac{450}{x}$ and $\frac{150}{x}$ are complementary angles.
Thus, $\frac{450}{x}$ + $\frac{150}{x}$ = 90$^{\circ}$
Since denominators are same (x), thus we can directly add the numerators ( 450 and 150)
Thus, $\frac{450}{x}$ + $\frac{150}{x}$ = $\frac{600}{x}$
Given $\frac{600}{x}$ = 90$^{\circ}$ ,
Thus x = $\frac{600}{90}$$^{\circ}$ = $\frac{20}{3}$$^{\circ}$ = 6.667$^{\circ}$ or = 6$\frac{2}{3}$$^{\circ}$
Thus $\frac{450}{x}$ = 450 $\div$ $\frac{20}{3}$ = 450 $\times$ $\frac{3}{20}$ = 67.5$^{\circ}$
$\frac{150}{x}$ = 150 $\div$ $\frac{20}{3}$ = 150 $\times$ $\frac{3}{20}$ = 22.5$^{\circ}$
