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

Let us assume the complementary angles be p and q,

We know that, sum of measures of complementary angle pair is 90^o.

Then,

= p + q = 90^o

It is given in the question that p > 45^o

Adding q on both the sides,

= p + q > 45^o + q

= 90^o > 45^o + q

= 90^o – 45^o > q

= q < 45^o

Hence, its complementary angle is less than 45^o.