Final answer:
The measures of two supplementary angles are found, where one angle is four times the measure of the other, resulting in one angle being 36 degrees and the other being 144 degrees.
Step-by-step explanation:
The student is tasked with finding the measures of two supplementary angles where one angle is four times the measure of the other. To solve this problem, we apply the concept that the sum of supplementary angles is 180 degrees. Let the measure of the smaller angle be x degrees. Therefore, the measure of the larger angle is 4x degrees. Now, we set up an equation based on the definition of supplementary angles: x + 4x = 180 degrees.
Simplifying this equation, we get 5x = 180 degrees, and by dividing both sides by 5, we find x = 36 degrees. This is the measure of the smaller angle. The larger angle, being four times this, is 4x or 4 × 36 degrees, which equals 144 degrees.
Thus, the measures of the two angles are 36 degrees for the smaller angle and 144 degrees for the larger angle.