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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 $45^{\circ}$.
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