Final answer:
The measure of the angle is 17 degrees, and the measure of its supplementary angle is 163 degrees.
Step-by-step explanation:
In this problem, we are given that an angle measures 146 degrees less than its supplementary angle.
Let's assume that the measure of the angle is x degrees. The measure of its supplementary angle will be 180 degrees - x degrees.
According to the given information, x = (180 - x) - 146.
Simplifying the equation, we get 2x = 34, which gives x = 17 degrees.
Therefore, the measure of the angle is 17 degrees, and the measure of its supplementary angle is 180 - 17 = 163 degrees.