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X+y =w+g-2xu=4xy-y=u

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