What is the measurement of <C if is rotated 19° clockwise?

To find the measurement of angle C after being rotated 19° clockwise, we can set up a right triangle using points A, B, and C as the vertices.

The length of AB can be found using the distance formula:
d = √[(x2 - x1)^2 + (y2 - y1)^2]

AB = √[(5 - 2)^2 + (2 - 5)^2]
AB = √[3^2 + (-3)^2]
AB = √[9 + 9]
AB = √18
AB ≈ 4.24

Now, we can find the tangent of the angle formed by AB and BC:
tanθ = opposite/adjacent
tanθ = 3 / -3
tanθ = -1

To find the measurement of angle C, we can use the arctan function:
θ = arctan(-1)
θ ≈ -45°

Since we are rotating this angle 19° clockwise, we need to subtract 19° from -45°:
C = -45° - 19°
C = -64°

Therefore, the measurement of angle C after being rotated 19° clockwise is 64°, if A=(2,5), B=(5,2), and C=(2,2).