Question
If the supplement of an angle is three times its complement, find the angle.
✓
Answer
Let the measure of the angle be $x^{\circ} .$
$ \therefore$ Its supplement will be $(180-x)^{\circ}$.
And its complement will be $(90- x )^{\circ}$. It is
given that $(180-x)^{\circ}=3(90-x)^{\circ} $
$\Rightarrow 180-x=270-3 x $
$\Rightarrow 2 x=90 $
$\Rightarrow x=45$
$\therefore$ The measure of the angle will be $45^{\circ}$.
$ \therefore$ Its supplement will be $(180-x)^{\circ}$.
And its complement will be $(90- x )^{\circ}$. It is
given that $(180-x)^{\circ}=3(90-x)^{\circ} $
$\Rightarrow 180-x=270-3 x $
$\Rightarrow 2 x=90 $
$\Rightarrow x=45$
$\therefore$ The measure of the angle will be $45^{\circ}$.
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