The measures of two angles have a sum of 180°. The measures of the angles are in a ratio of 4:1. Determine the measures of
both angles. Define a variable to show your work

Since it is given that the angle measures are in a 4:1 ratio, make them variables. You would have 4x and X. Now, because they are equal to 180 degrees you have to do 4x+x = 180. Combine the like-terms and solve for x. (X=36). Then, since the angle measures were 4x and X all that is left is to plug in. Since x=36 that is one angle measure and when you do 4*36 to find the other the answer is 144. Therefore the angle measures are 144 degrees and 36 degrees.