Question

An angle is equal to two-third of its supplements. Find its measure.

Answer 1

Let x and y be the two angles

They are supplement means $x+y=180$${}^{\circ }$

Now one angle is two third of another which

means $x=2y/3$

putting in to equation

$\frac{2y}{3}+y={180}^{\circ }$

$\Rightarrow \frac{2y+3y}{3}={180}^{\circ }$

$\Rightarrow 5y=180\times 3$

$\Rightarrow y=\frac{180\times 3}{5}$

$\Rightarrow y=108$

$y=108$

$x=\frac{2y}{3}=\frac{2\cdot 108}{3}=72$

$\therefore x=72$ and $y=108$.