# Why can two acute angles be supplementary?

Dec 6, 2015

They cannot.
Their sum must be ${180}^{o}$ to be supplementary, but it will be less than ${180}^{o}$ because each acute angle is less than ${90}^{o}$.

#### Explanation:

Angles $\angle A$ and $\angle B$ are supplementary if their sum measures ${180}^{o}$.

Acute angle are those measured less than ${90}^{o}$.

If $\angle A < {90}^{o}$ and $\angle B < {90}^{o}$ then
$\angle A + \angle B < {180}^{o}$

Therefore, two acute angle cannot be supplementary to each other.