Question

the measure of two supplementary angles are in the ratio 4:5 what are the measures of the two angles

Answer 1

When you are given two quantities in a ratio, and the quantities are unknown, just add an x to the ratio numbers. Then follow what the problem tells you.
The supplementary angles are in a ratio of 4:5.
Write the x's: the supplementary angles are in a ratio of 4x:5x.
Since the angles are supplementary, their measures add up to 180, so
4x + 5x = 180
Solve for x.
Then one angle is 4x and the other angle is 5x.