An angle is greater than $45^{\circ}$. Is its complementary angle greater than $45^{\circ}$ or equal to $45^{\circ}$ or less than $45^{\circ}$?

Given:

An angle is greater than $45^{\circ}$. 

To do:

We have to find whether its complementary angle is greater than $45^{\circ}$ or equal to $45^{\circ}$ or less than $45^{\circ}$.

Solution:

Given angle is greater than $45^{\circ}$

Let the given angle be $x^{\circ}$

This implies,

$x^{\circ} > 45^{\circ}$

Complement of $x=90^{\circ}-x^{\circ}$

Therefore,

Complement of $x< 45^{\circ}$      [Since $x^{\circ} > 45^{\circ}$]

Hence, the required angle is less than $45^{\circ}$.