Question

An angle is greater than $45\degree$ . Is its complementary angle greater than $45\degree$ or equal to $45\degree$ or less than $45\degree$ ?

Answer 1

Let the complementary angles be $x$ and $y$ i.e., $x + y = 90\degree$
It is given that $x > 45\degree$
Adding $y$ both sides, $x + y > 45\degree+ y$
$\Rightarrow 90\degree > 45\degree+ y$
$\Rightarrow 90\degree- 45\degree> y$
$\Rightarrow y < 45\degree$

Thus, its complementary angle is less than $45\degree$

Read more: Supplementary and Complementary Angles