Question

the measure of two complimentary angles is in the ratio 1:4. what are the degree measure of the two angles?

Answer 1

If two angles are supplementary it means they add up to 180 degrees (ie they make a straight line.)
If the ratio of both angles is 1:4, then that means the bigger angle is four times the size of the smaller. Using that, you can add variables. The smaller andle is x (or 1x) and the bigger one would be four times that, so 4x. If you add the two angles together, you get 180.
Therefore:
x+4x=180


5x=180
divide both side by 5 to get
x=36
substitute this in for your original formulas of x and 4x
x=36, the smaller angle is 36 degrees
4x= 4(36)= 144, the larger angle is 144 degrees