## Angle between line and plane

Determine the angle between the line with symmetric equations x=-y, z=4 and the plane 2x-2z=5.

so the direction vector for the sym equation is.. (1,1, ?)
for the z.. I tried with 1, but then I didn't get the answer. So I tried with z=4 and I got -30 degrees as the answer, and the back of the book has 30 degrees. Is this z value in the direction value correct? I don't think it is right because the final answer is positive, not negative 30. Also, z=4 as the sym equation doesn't indicate that the direction value should have a z=4..

I am confused about this. Can someone let me know what the direction value should be?

Here is my work below:

sin(theta)=(n . d)/ (|n||d|)
(1,1,4). (2,0,-2)
---------------
(sqrt(18x8))
theta= - 30 degrees

the final answer is positive 30 degrees like i said, but i cant seem to get this.. where is my error? thanks in advance.