Question:
Find the measure of an angle which is $30^{\circ}$ less than its supplement.
Solution:
Let the measure of the angle be $x^{\circ}$.
$\therefore$ Supplement of $x^{\circ}=180^{\circ}-x^{\circ}$
It is given that,
$\left(180^{\circ}-x^{\circ}\right)-x^{\circ}=30^{\circ}$
$\Rightarrow 180^{\circ}-2 x^{\circ}=30^{\circ}$
$\Rightarrow 2 x^{\circ}=180^{\circ}-30^{\circ}=150^{\circ}$
$\Rightarrow x^{\circ}=75^{\circ}$
Thus, the measure of the angle is $75^{\circ}$.