Saying arccos(-√2/2) is the same as saying cos(x)=-√2/2. This is one the trigonometric values you should have memorized if you are taking a a trig class. In order to get √2/2, x must be equal to 45° or pi/4. But since it is a negative √2/2, the answer would be -45°or -pi/4.
There are technically multiple answers to this, but since you weren't given a range for the answers, I would stick with -45°.
Hope this helps