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