Question

An angle is greater than ${45}^{\circ }$ then its complementary angle is _________ than ${45}^{\circ }$.

Answer 1

We know, two angles are said to be complementary, if the sum of their measures is ${90}^{\circ }.$

Given, one angle is greater than ${45}^o$.

Let the angle be ${45}^o+x$.

Then, its complementary angle is ${90}^o-({45}^o+x)$

$={90}^o-{45}^o-x={45}^o-x$, which is clearly less than ${45}^o$.

Hence, an angle is greater than ${45}^o$, then its complementary angle is less than ${45}^o$.