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If the supplement of an angle is three times its complement, find the angle.
Given:
The supplement of an angle is three times its complement.
To do:
We have to find the measure of the angle.
Solution:
Two angles are said to be supplementary if the sum of their measures is $180^o$.
Two angles are said to be complementary if the sum of their measures is $90^o$.
Let the required angle be $x$.
This implies,
The measure of the complementary angle $=90^o-x$
The measure of the supplementary angle $=180^o-x$
According to the question,
$180^o-x=3(90^o-x)$
$180^o-x=270^o-3x$
$3x-x=270^o-180^o$
$x=\frac{90^o}{2}$
$x=45^o$
The measure of the required angle is $45^o$.
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