Question

An angle is greater than 45° . Is its complementary angle greater than 45° or equal to 45° or less than 45° ?

Answer 1

Let the complementary angles be x and y, 

i.e., x+ y = 90 

It is given that x > 45 

Adding y both sides,

x + y >45+y

⇒90 > 45 + y 

⇒ 90 - 45 > y 

⇒ y < 45

Thus, its complementary angle is less than 45 .