Answer + Explanation:
First, find what the sum of the interior angles must be. You can use the formula 180(n - 2) where n is the number of sides to find this.
n = 5, so 180( 5 - 2) = 180 * 3 = 540 degrees.
Then, you can add up all the interior angles of the pentagon and it will add to 540. This means that:
2x + x + 2x + 90 + 90 = 540
5x + 180 = 540
5x = 360
x = 72
Then you can go through and find the measure of each angle:
S = 90 degrees (given)
T = 2x = 2 * 72 = 144 degrees
U = x = 72 degrees
V = 2x = 72 * 2 = 144 degrees
W = 90 degrees (given)