Final answer:
The question pertains to finding the measure of an unknown angle using the concepts of complementary and supplementary angles. Upon setting up and solving the given equation, the measure of the angle is found to be 70 degrees.
Step-by-step explanation:
Let's denote the unknown angle by A. Its complement will be 90 - A, as complementary angles add up to 90 degrees. Its supplement will be 180 - A, as supplementary angles add up to 180 degrees. Given that five times its complement (5*(90 - A)) is 60 degrees less than twice its supplement (2*(180 - A) - 60), we can set up the equation :
5 * (90 - A) = 2 * (180 - A) - 60
Solving this equation, we find that A = 70 degrees. Therefore, the measure of the angle is 70 degrees.
Learn more about Complementary and Supplementary Angles