Question

Choose the correct word and fill in the blanks :

If an angle is greater than $45°$, then its complementary angle is …………. than $45°$. (less / greater)

Answer 1

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.

As per the question :

Let the given angle is $50°$. ($\because$it is given as angle is greater than $45°$)

Then its complementary angle = $90°-50°=40°$ ($\because$Complementary angles add up to $90°$)

As we have calculated the complementary angle of the given angle is $40°$ which is less than $45°$.

Hence, if an angle is greater than $45°$, then its complementary angle is less than $45°$.