Question

Two acute angles can be supplementary. Say True/False.

• A. True
• B. False

Answer 1

The correct option is B

False

Consider two angles - $\angle$ABC and $\angle$XYZ. Suppose one of them, say $\angle$ABC, is a right angle. For the pair to be supplementary, the other angle has to be 90${}^{\circ }$. Now, if we reduce the angle of $\angle$ABC even by a small amount, say 1${}^{\circ }$, this has to be added to the other angle $\angle$XYZ to make sure that their sum is constant. In this case, we have the following values of $\angle$ABC and $\angle$XYZ –

$\angle$ABC = 89${}^{\circ }$ [acute]

$\angle$XYZ = 91${}^{\circ }$ [obtuse]

So, it is impossible to have both the angles acute to constitute a pair of supplementary angles. Hence the answer is False.