Is it possible for two acute angles to be supplementary?

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Is it possible for two acute angles to be supplementary?

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Answer 1 · 2016-01-01T12:00:12

No.

Explanation:

An acute angle means that it is less than $90^{o}$ $90^o$ ( $α < 90^{o}$ $alpha < 90^o$ ) or $\frac{π}{2}$ $pi/2$ in radians,

If two angles are supplementary, it means that their sum is $180^{o}$ $180^o$ ( $x + y = 180^{o}$ $x+y = 180^o$ ) or $π$ $pi$ in radians.

Now, if two angles are acute, i.e., less than $90^{o}$ $90^o$ ( $a < 90^{o}$ $a<90^o$ and $b < 90^{o}$ $b<90^o$ ), their sum must be less than $180^{o}$ $180^o$ :
$a < 90^{o}$ $a<90^o$
$b < 90^{o}$ $b<90^o$
_____
$a + b < 180^{o}$ $a+b<180^o$

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Is it possible for two acute angles to be supplementary?

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