SOLUTION: If two supplementary angles are in the ratio of 5:4, what is the measure of the larger angle? PLEASE show me how to do this as well.

Hi, there--

THE PROBLEM:
If two supplementary angles are in the ratio of 5:4, what is the measure of the larger angle? PLEASE show me how to do this as well.

A SOLUTION:
Two angles are supplementary if the sum of their measures is 180.

Let x be the measure of the smaller angle.
The measure of the second angle is 180 minus the measure of the smaller one, or 180-x.

We know that the ratio of the two angle measures is 5:4. We can build a proportion of two ratios
comparing the measure of the larger angle to the measure of the smaller angle.



We want to rewrite this equation without the denominators, to make it easier to solve. I show you this in 
two steps, but you can combine them if you understand what's happening. 

First Step: Multiply both sides of the equation by 4 to clear the denominator on the left.



Second Step: Multiply both sides of the equation by x to clear the denominator on the right.




(Note: You could have just multiplied both sides by 4x in a singe step.)

Now simplify and solve for x.


Add 4x to both sides to combine the x-terms on the left.



Divide both sides by 9. (9x/9 is x.)



In the context of this problem, x=80 means the smaller angle has a measure of 80 degrees.

Since the angles are supplementary, the larger angle has a measure of 100 degrees (180-80=100.)
The ratio of 100:80 is equivalent to the ratio 5:4 because they differ by a scale factor of 20.




Hope this helps! Feel free to email if you have any questions about the solution.

Good luck with your math,

Mrs. F
math.in.the.vortex@gmail.com