Find the angle whose supplement is four times its complement.

Let the measure of the required angle be $x^{\circ}$

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

And, measure of its supplement $=(180-x)^{\circ}$.

Therefore,

$(180-x)=4(90-x)$

$\Rightarrow 180-x=360-4 x$

$\Rightarrow 3 x=180$

$\Rightarrow x=60$

Hence, the measure of the required angle is $60^{\circ}$.