### Instruction: The measures of a pair of supplementary angles are in the ratio of 7:2. How many degrees are in the measure of their positive difference?### Response: To find the positive difference of the measures of the supplementary angles, I need to first find the measures of each angle.
I can use the fact that supplementary angles add up to 180 degrees, and that their ratio is 7:2.
Let me call the larger angle 7x and the smaller angle 2x, where x is some positive constant.
Then, I have the equation 7x + 2x = 180, which I can simplify and solve for x.
I get 9x = 180, so x = 20.
This means that the larger angle is 7x = 7 * 20 = 140 degrees, and the smaller angle is 2x = 2 * 20 = 40 degrees.
The positive difference of their measures is 140 - 40 = 100 degrees.