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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Updated on: 10-Oct-2022

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