Question

Choose the correct word and fill in the blanks :

Two acute angles ………… be complementary angles. (can / cannot)

Answer 1

Acute angle :

An acute angle is an angle that measures between $0°$ and $90°$.

Complementary angles :

As we know that, two angles are said to be complementary angles if they add up to $90°$. As given in the figure :

The sum of $\angle AOB$ and $\angle BOC$ is $90°$.( i.e. $\angle AOB+\angle BOC=20°+70°=90°$)

So, $\angle AOB$ and $\angle BOC$ are complementary angles.

Here, the measure of$\angle AOB$ and $\angle BOC$ is less than $90°$ i.e. both are acute angles.

So if one angle is an acute angle then its complementary angle will also be an acute angle because the sum of two acute angles can be $90°$.

Hence two acute angles can be complementary angles.