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If the supplement of an angle is two-third of itself Determine the angle and its supplement.
Given:
The supplement of an angle is two-third of itself.
To do:
We have to find the angle and its supplement.
Solution:
Two angles are said to be supplementary if the sum of their measures is $180^o$.
Let the required angle be $x$.
This implies,
The measure of the supplementary angle $=\frac{2}{3}x$
Therefore,
$x+\frac{2}{3}(x)=180^o$
$\frac{3x+2x}{3}=180^o$
$\frac{5x}{3}=180^o$
$x=\frac{3}{5}\times180^o$
$x=3\times36^o$
$x=108^o$
$\frac{2}{3}x=\frac{2}{3}(108^o)=72^o$
The measures of the required angle and its supplement are $108^o$ and $72^o$ respectively.
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