Two angles of a quadrilateral are supplementary. One of them is 4 less than twice the other. What is the measure of the larger angle?

x + 2x-4 = 180

x+y=180

To find the measure of the larger angle, let's assign variables to the unknown angles of the quadrilateral. Let's call one of the angles x.

According to the problem, the other angle is 4 less than twice the first angle. So, the measure of the other angle can be represented as 2x - 4.

Since the two angles are supplementary, their sum is 180 degrees. Therefore, we can write the equation:
x + (2x - 4) = 180

Simplifying the equation:
3x - 4 = 180
3x = 184
x = 184/3

Now, we need to find the larger angle by substituting the value of x into one of the expressions we obtained earlier. Let's use 2x - 4:
2(184/3) - 4 = 368/3 - 4 = (368 - 12)/3 = 356/3

Thus, the measure of the larger angle is 356/3 degrees.