Let A and B be the two complementary angles.
A = smaller angle = 2x
B = larger angle = 13x
x = some unknown number
Note how the ratio A:B turns into 2x:13x which simplifies to 2:13
A+B = 90 ... because the angles are complementary
2x+13x = 90 ... substitution
15x = 90
x = 90/15
x = 6
A = 2*x = 2*6 = 12 degrees
B = 13*x = 13*6 = 78 degrees
The two angles are 12 degrees and 78 degrees.
Check:
A/B = 12/78 = (2*6)/(13*6) = 2/13, so A:B = 2:13
A+B = 12+78 = 90
