Angle a measures 50 degrees, if angle a is rotated 45 degrees, what is the measurement of angle a

Rotations preserve lengths, angles, area, volumes, etc. In other words, they are rigid trasformation.

So, if you rotate an angle of a given measure, the angle will remain the same measure.

For example, think of a pizza, spliced in four pieces (so you have four right angles). If you spin the pizza around, the four slices will still have a right angle each!