Mathematics

The supplementary angle of an angle is one third of the angle. Then the angle and its supplement are __________.


ANSWER

$$135^o, 45^o$$


SOLUTION
Let the angle is $$x$$, and its supplementary angle is $$\dfrac{1}{3}x$$.
We know that the sum of the supplementary angles is $$180^o$$, then
$$x+\dfrac{1}{3}x=180^o\\ \Rightarrow \dfrac{4}{3}x=180$$
$$\Rightarrow x=\dfrac{180\times 3}{4}=135^o$$
It's supplementary angle $$=\dfrac{135}{3}=45^o$$
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