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An angle is $\frac{2}{3}$ of its supplement. What is its magnitude?
Given :
An angle is $\frac{2}{3}$ of its supplement.
To do :
We have to find the magnitude of the angle.
Solution :
Supplementary angles:
Two angles are said to be supplementary if the sum of their measures is 180°.
Let the measure of the supplementary angle be x.
This implies,
The measure of the given angle $= \frac{2}{3}(x)$.
Therefore,
$x +\frac{2}{3} x = 180°$
$\frac{(3+2)}{2} x = 180°$
$\frac{5}{3} x = 180°$
$5x = 3(180°)$
$5x = 540°$
$x = \frac{540°}{5}$
$x = 108°$
Therefore, the measures of the angles are 108° and $\frac{2}{3}(108)° = 2(36)° = 72°$.
The magnitude of the required angle is 72°.
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