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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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