The measure of an angle is three times the measure of its complement. The angles are:

The correct option is D ${22.5}^{\circ },{67.5}^{\circ }$
Let the complement be $x$.

Then the angle $=3x$.

We know, the sum of the complementary angles is ${90}^{\circ }$

$\Rightarrow x+3x={90}^{\circ }\Rightarrow 4x={90}^{\circ }\Rightarrow x={22.5}^{\circ }$.

Hence, the angles are:

$x=1\times {22.5}^{\circ }={22.5}^{\circ }$

and $3x=3\times {22.5}^{\circ }={67.5}^{\circ }$.

Hence, option $D$ is correct.