An angle is greater than 45o0. Is its complementary angle greater than 45o or equal to 45o or less than 45o?

Dear Student

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.

Thanks