Introduction:
An angle and its complementary angle are two angles that add up to 90 degrees. In this case, we are given that the angle is greater than 45 degrees, and we need to determine whether its complementary angle is greater than 45 degrees, equal to 45 degrees, or less than 45 degrees.

Understanding Complementary Angles:
Complementary angles are two angles that when added together, result in a right angle, which measures 90 degrees. Let's assume the given angle is A. The complementary angle to A is denoted as angle B, and we know that A + B = 90 degrees.

Exploring the Possibilities:
To determine the relationship between the given angle and its complementary angle, we need to consider the possible values for angle A, which is greater than 45 degrees. Let's analyze each possibility:

1. Angle A is greater than 45 degrees and less than 90 degrees:
If angle A is greater than 45 degrees but less than 90 degrees, then its complementary angle B must be less than 45 degrees. The reason is that the sum of angle A and angle B must be 90 degrees, so if angle A is already greater than 45 degrees, angle B needs to be less than 45 degrees to compensate and fulfill the condition A + B = 90 degrees.

2. Angle A is equal to 90 degrees:
If angle A is equal to 90 degrees, it cannot have a complementary angle because the sum of the two angles would exceed 90 degrees. In this case, the complementary angle would be undefined.

3. Angle A is greater than 90 degrees:
If angle A is greater than 90 degrees, it cannot have a complementary angle because the sum of the two angles would exceed 90 degrees. Similar to the previous case, the complementary angle would be undefined.

Conclusion:
Based on the possibilities explored, we can conclude that if the given angle is greater than 45 degrees, its complementary angle will always be less than 45 degrees. This is because the sum of the two angles must equal 90 degrees, and if the given angle is already greater than 45 degrees, the complementary angle needs to be less than 45 degrees to satisfy this condition.

Less than 45 degree