Angle XYZ is rotated 270 degrees counterclockwise about the origin to form angle X′Y′Z′. Which statement shows the measure of angle X′Y′Z′a. m∠X′Y′Z′ = m∠XYZb. m∠X′Y′Z′ = 180 degreesc. m∠X′Y′Z′ = 270 degreesd. m∠X′Y′Z′ = 2 × m∠XYZ

a. m∠X′Y′Z′ = m∠XYZ
       
Rotating the angle doesn't change the measurement of the angle, it merely changes the location on the graph where the angle is. To show you a real world example of this, imagine the following. Take a sheet of graph paper and on top of that graph paper, place a piece of clear plastic. Now take a pin and push it through the plastic into the graph paper at the origin. Now take a marker and draw an angle on the clear plastic. That angle you drew can be considered â XYZ. Now finally, rotate the piece of plastic any number of degrees clockwise, or counterclockwise. Does the measurement of the rotated angle ever change? The answer to that question is "No. It always stays the same." And the exact same concept applies to the rotation of angle XYZ in this problem.