#### Answer

The angles are 32° and 58°.

#### Work Step by Step

Let X represent one of the angles.
The other one is 6° smaller than twice the other angle.
Twice the other angle means 2 $\times$ X = 2X.
6° smaller than twice the other angle means 2X - 6.
Since the sum of two complementary angles is 90°, one of the angles is X and the other 2X - 6. This lets us set up the following equation:
X + 2X - 6 = 90
3X - 6 = 90
Add 6 to both sides
3X = 96
Divide both sides by 3
X = 32
Since X = 32, the first angle is 32°, while the second angle is 2 $\times$ 32 - 6 = 58°