Find the angle which is four times its complement.

Let the measure of the required angle be $x$.

Then, measure of its complement $=\left(90^{\circ}-x\right)$.

Therefore,

$x=\left(90^{\circ}-x\right) 4$

$\Rightarrow x=360^{\circ}-4 x$

$\Rightarrow 5 x=360^{\circ}$

$\Rightarrow x=72^{\circ}$

Hence, the measure of the required angle is $72^{\circ}$.