Find the measure of an angle which is
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 $75^{\circ}$.