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 $75^{\circ}$.

 

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