Question
Which angle is equal to two-third of its supplement?
✓
Answer
Let the angle be $x$ According to the problem,
$ x=\frac{2}{3} \times\left(180^{\circ}-x\right)$
$3 x=2\left(180^{\circ}-x\right)$
$3 x=360^{\circ}-2 x$
$3 x+2 x=360^{\circ}$
$5 x=360^{\circ}$
$x=\frac{360^{\circ}}{5}$
$x=72^{\circ} $
$\therefore$ The angle is $72^{\circ}$
$ x=\frac{2}{3} \times\left(180^{\circ}-x\right)$
$3 x=2\left(180^{\circ}-x\right)$
$3 x=360^{\circ}-2 x$
$3 x+2 x=360^{\circ}$
$5 x=360^{\circ}$
$x=\frac{360^{\circ}}{5}$
$x=72^{\circ} $
$\therefore$ The angle is $72^{\circ}$
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