Mathematics

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


SOLUTION
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 

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

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

$$\Rightarrow 5y=180\times 3$$

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

$$\Rightarrow y=108$$

$$ y = 108 $$

$$x=\dfrac {2y}3=\dfrac{2\cdot108}{3}=72$$

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