#### Answer

62 degrees, 118 degrees

#### Work Step by Step

If two angles are supplementary, their sum is $180$ degrees.
Also, since the difference between their measures is $56$ degrees, one angle is $56$ degrees greater than the other.
If we let the smaller unknown angle be $x$ degrees, the larger unknown angle must be $x+56$ degrees.
$x+(x+56)=180$
$2x+56=180$
$2x=180-56$
$2x=124$
$x=\frac{124}{2}$
$x=62$
Therefore, one of the angles is $62$ degrees while the other angle is $62+56=118$ degrees.