The value of angle RUS is equal to 116 degrees.
The rectangle in the image is a rhombus. Thus, all angles in the rectangle are equal to 90 degrees and adjacent sides are equal. Thus, we have mRUS = 90 - 64 = 26 degrees.
In the given rectangle QRST, we are given that angle QRS is 64 degrees.
We need to find the measure of angle RUS.
Since QRST is a rectangle, we know that angles QRS and RUS are supplementary angles, which means that they add up to 180 degrees.
Therefore, we can write the following equation:
x + 64 = 180
Subtracting 64 from both sides of the equation, we get:
x = 180 - 64
x = 116 degrees
Therefore, the measure of angle RUS is 116 degrees.
Another way to solve this problem is to use the fact that opposite angles in a rectangle are equal.
We know that angle QRS and angle TSU are opposite angles, so they must be equal.
Therefore, we can write the following equation:
64 degrees = x degrees
Solving for x, we get:
x = 64 degrees