Question

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

Answer 1

Let $\angle a\text{and}\angle b$ be the two complementary angles.

So, $\angle a+\angle b={90}^{\circ }$

$\Rightarrow \angle b={90}^{\circ }-{45}^{\circ }={45}^{\circ }$

This means both angles are equal to ${45}^{\circ }$.

Now , let $\angle a>{45}^{\circ }$, say $\angle a={46}^{\circ }$

$\Rightarrow \angle b={90}^{\circ }-{46}^{\circ }={44}^{\circ }$

This means if we increase $\angle a$, $\angle b$ will decrease and thus will be less than ${45}^{\circ }$.

Hence, we can say that if an angle is greater than ${45}^{\circ }$, its complementary angle will be less than ${45}^{\circ }$.