Mathematics

# The measure of an angle is four times the measure of its supplementary angle. Then the angles are __________.

$36^o, 144^o$

##### SOLUTION
Two angles are called to be supplementary if the summation of both angles is $180^{\circ}$.
say $\angle A$ and $\angle B$ are supplementary angles
$\Rightarrow$          $\angle A$ $+$ $\angle B$ $=180^{\circ}$
$\because \angle A = 4\times \angle B$        (Given in question)
so,  $4\times \angle B$ $+$ $\angle B$ $=180^{\circ}$
$\Rightarrow$            $5\times \angle B$   $=180^{\circ}$
$\Rightarrow$                   $\angle B$   $=36^{\circ}$
Now, $\angle A = 4\times \angle B$
$\Rightarrow$   $\angle A$   $=4\times36^{\circ}$
$\Rightarrow$   $\angle A$   $=144^{\circ}$
so these angles are $36^{\circ}$, $144^{\circ}$
Hence the option $(A)$ $36^{\circ}$, $144^{\circ}$ is correct.

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Single Correct Medium Published on 09th 09, 2020
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