One of two supplementary angles is five times the measure of the other. find the measure of the smaller angles.

Since we know that supplementary angles are angles that add up to 180 degrees, and one of the angles is 5 times the other, our equation would look like this: 5x + x = 180. 
We then combine like terms so that the equation will look like this: 6x=180
We then divide both sides by 6 so that we get to our x=30 which is the measure of the smaller angle.