Question

Two acute angles can be supplementary.

• 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 $\angle XYZ$ –

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

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

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

Hence the answer is False.