Need an Explanation for the Correct Final Answer

Question

I was solving the problem below and my answer was 56 degrees but, in the answer key, it was 180-56=124 degrees as the final answer. Can someone explain why 56 was subtracted from 180? Apologies if my question seems too simple.

Answer 1

Let $\theta$ be the angle between $\vec{A}$ and $\vec{B}$. Then : $$\vec{A} \cdot \vec{B} = \|\vec{A}\|\|\vec{B}\| \cos(\theta) = -6$$ and : $$\|\vec{A} \times \vec{B}\| = \|\vec{A}\|\|\vec{B}\|\ |\!\sin(\theta)| = 9.$$ This yields : $$\frac{|\!\sin(\theta)|}{\cos(\theta)} = -\frac{3}{2}.$$ The angle $\theta$ then has to be in the second or third quadrant for the cosine to be negative. There are two solutions now, either $180° - \arctan(-3/2)$ or $180° - \arctan(3/2)$, depending on the sign of $\sin(\theta)$.