The difference of two complementary angles is . Then, the angles are:
Step 1: Explanation of correct options.
Determine the pair of complementary angles with a difference of .
Option (A) :
Assume that the angles are
The sum of complementary angle is .
So, .
Also, the difference of the angles is .
So,
Add both the obtained equations and simplify:
Substitute into and solve:
So, the angles are and option (A) is correct.
Step 2: Explanation for incorrect options.
Option (B) :
The sum of the angles is
The angles are not complementary.
So, option (B) is incorrect.
Option (C) :
The sum of the angles is
The angles are not complementary.
So, option (C) is incorrect.
Option (D) :
The sum of the angles is
The angles are not complementary.
So, option (D) is incorrect.
Hence, (A) is the correct option.