Vector A has a magnitude of 6 and is at an angle of 32.4 degrees measured counter-clockwise from the x axis. Vector B has a magnitude of 12 and is at an angle of 113.8 degrees measured counter-clockwise from the x axis. Vector C has a magnitude of 17 and is at an angle of 180 degrees measured counter-clockwise from the x axis. Lastly, Vector D has a magnitude of 17 and is at an angle of 281.7 degrees measured counter-clockwise from the x axis. If R = A + B + C - D, find the angle R makes with the x axis measured counterclockwise in degrees.

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To find the angle R makes with the x-axis, we need to add up the x-components and y-components of vectors A, B, C, and D, and then find the resultant angle.

First, let's find the x and y components of vectors A, B, C, and D using trigonometry.

For vector A:
Magnitude of A = 6
Angle of A = 32.4 degrees

Using trigonometry, we can find the x and y components of A using the following formulas:
Ax = Magnitude of A * cos(Angle of A)
Ay = Magnitude of A * sin(Angle of A)

Ax = 6 * cos(32.4)
Ay = 6 * sin(32.4)

Similarly, we can find the x and y components of vectors B, C, and D using their magnitudes and angles.

For vector B:
Magnitude of B = 12
Angle of B = 113.8 degrees

Bx = 12 * cos(113.8)
By = 12 * sin(113.8)

For vector C:
Magnitude of C = 17
Angle of C = 180 degrees

Cx = 17 * cos(180)
Cy = 17 * sin(180)

For vector D:
Magnitude of D = 17
Angle of D = 281.7 degrees

Dx = 17 * cos(281.7)
Dy = 17 * sin(281.7)

Next, we add up the x-components and y-components separately to find the resultant vector R.

Rx = Ax + Bx + Cx - Dx
Ry = Ay + By + Cy - Dy

Finally, we can find the angle R makes with the x-axis using the formula:
Angle of R = arctan(Ry / Rx)

Calculate Rx and Ry using the formulas above, and then find the angle R using the arctan function.