Final answer:
The measure of the angle whose complement is 1/10 of its supplement is 80 degrees. This is found by setting up an equation based on the angle relationships and solving for the unknown angle.
Step-by-step explanation:
To find the measure of an angle whose complement is 1/10 of its supplement, we can set up a system of equations based on the angle relationships. Let x represent the measure of the unknown angle. Since complementary angles sum up to 90 degrees and supplementary angles sum up to 180 degrees, we have two relationships:
- The complement of the angle is 90 - x.
- The supplement of the angle is 180 - x.
According to the problem, the complement is 1/10 of the supplement, which can be written as an equation:
90 - x = 1/10(180 - x)
Multiplying both sides by 10 to clear the fraction, we get:
900 - 10x = 180 - x
Now we combine like terms to solve for x:
900 - 180 = 10x - x
720 = 9x
Finally, divide by 9:
x = 80 degrees
Thus, the angle measures 80 degrees.