What is the number of degrees in the measure of the larger of two supplementary angles if the ratio of their measures is 4:5?

4x + 5x = 180

9x = 180
x = 20
substituting,
4x = 4*20 = 80 degrees
5x = 5*20 = 100 degrees

hope this helps~ :)

To find the number of degrees in the measure of the larger of two supplementary angles, we need to find the measures of both angles.

Let's assume the measure of the smaller angle is 4x degrees and the measure of the larger angle is 5x degrees since the ratio of their measures is 4:5.

Since the angles are supplementary, the sum of their measures is 180 degrees. So, we can set up an equation:

4x + 5x = 180

Combining like terms, we get:

9x = 180

Next, we need to solve for x. We can divide both sides of the equation by 9:

9x/9 = 180/9

Simplifying, we find:

x = 20

Now that we have the value of x, we can substitute it back into the expressions for the angles' measures:

Measure of the smaller angle = 4x = 4 * 20 = 80 degrees
Measure of the larger angle = 5x = 5 * 20 = 100 degrees

Therefore, the number of degrees in the measure of the larger angle is 100 degrees.