The measure of an angle is eighty-nine times the measure of its supplementary angle. What is the measure of each angle?

2 degrees and 178 degrees.

Step-by-step explanation:

So, remember if 2 angles are supplementary, they equal 180 degrees. Let's call the smaller angle x, meaning the bigger angle, which is 89 times the size of the smaller angle, would be 89x. Now let's put that into an equation.

180 = x + 89x

We now have to group the x's together:

180 = 90x

Now in order to determine x, we have to divide by 90 on both sides.

X = 2

So we know that the smaller angle is 2, meaning that if the larger angle is 89 times the size, the larger angle would be 178.