Two complementary angles are in the ratio 4 : 5. Find the angles.

Let the two angles be 4x and 5x, respectively.
Then,

$4 x+5 x=90$

$\Rightarrow 9 x=90$

$\Rightarrow x=10^{\circ}$

Hence, the two angles are $4 x=4 \times 10^{\circ}=40^{\circ}$ and $5 x=5 \times 10^{\circ}=50^{\circ}$.