Find the angle which is five times its supplement.

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

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

Therefore,

$x=\left(180^{\circ}-x\right) 5$

$\Rightarrow x=900^{\circ}-5 x$

$\Rightarrow 6 x=900^{\circ}$

$\Rightarrow x=150^{\circ}$

Hence, the measure of the required angle is $150^{\circ}$.