#### Answer

One angle is 45°.
The other angle is 135°.

#### Work Step by Step

Let x represent one angle.
The other one is 45 degrees smaller than four times the first angle.
Four times the other angle means 4x.
45 smaller than four times the other angle means 4x - 45.
So, one angle is x and the other 4x - 45.
Because the angles are supplementary, their sum is 180.
So, x + 4x - 45 = 180
5x - 45 = 180
5x = 225
Divide both sides by 5.
x = 45
One angle is 45°.
The other angle is 180 - 45 = 135°.