Two complementary angles differ by 34 degree find the angles

Answer 1

Let's call the two angles A and B.

Because two angles are complementary, we have A + B = 90 degrees.

And because the angles differ by 34 degrees, we have |A - B| = 34 degrees.

We can now set up a system of equations:

1) A + B = 90
2) |A - B| = 34

We can solve this system by considering two cases:

Case 1: A > B
In this case, A - B = 34
A + B = 90
2A = 124
A = 62 degrees
B = 28 degrees

Case 2: B > A
In this case, B - A = 34
B + A = 90
2B = 124
B = 62 degrees
A = 28 degrees

Therefore, the two angles are 28 degrees and 62 degrees.