Final answer:
The measure of the angle is 18 degrees.
Step-by-step explanation:
To solve this problem, we can set up an equation based on the given information. Let's suppose the angle is x. The supplement of the angle would be 180 - x. According to the problem, the angle is equal to one ninth of its supplement, so we have the equation x = (1/9)*(180 - x).
To solve for x, we can multiply both sides of the equation by 9, distribute, and then solve for x: 9x = 180 - x. Adding x to both sides gives us 10x = 180, and dividing by 10 gives us x = 18. Therefore, the measure of the angle is 18 degrees.