Imagine angles as two lines meeting at a point, forming a corner. Let's call one angle 'x' and its supplementary angle 'y'. This means that when you add angle x and angle y together, they will form a straight line, which is 180 degrees.
Now, the problem tells us that angle x is nine times the measure of angle y. This can be represented as x = 9y.
Since angle x and angle y are supplementary, we can write an equation: x + y = 180.
Substitute the value of x from the first equation into the second equation: 9y + y = 180.
Solve for y: 10y = 180, y = 18 degrees. Now, substitute y back into x = 9y to find x: x = 9 * 18 = 162 degrees.