#### Answer

65 degrees, 115 degrees

#### Work Step by Step

Since the two angles are supplementary, their sum is $180$ degrees.
Let the smaller angle be $x$. Since the larger angle is $15$ degrees less than twice the smaller angle, the expression for the larger angle is $(2x-15)$.
Since the sum of the two angles is 180, we obtain:
$x+(2x-15)=180$
$x+2x-15=180$
$3x-15=180$
$3x=180+15$
$3x=195$
$x=\frac{195}{3}=65$
Therefore, the smaller angle is $65$ degrees while the larger angle is $(2x-15)=2(65)-15=130-15=115$ degrees.