Find the measure of angle u in degrees. brainliest and 20 points

Since this triangle is a right triangle, and the lengths of the sides are included we can use trigonometry to determine the measure of angle U.

In case you're unsure of the trigonometric ratios remember: SOH CAH TOA
Sin. = opposite/hypotenuse, Cos. = adjacent/hypotenuse, Tan. = opposite/adjacent

Since all the side lengths are given, your choice of ratio will not affect the final answer. I will be using Tan. = opposite/adjacent.

Tan. of angle U = 77/36 = 2.13888888889
Now you can refer to a trigonometric table to see which angle degree is most similar to the decimal above.
In this case the angle is around 65 degrees.