anglegeometrygraphing-functions
Let's say we have a line $y=-x+2$, and we have to find the angle this line makes with the positive sense of the $x$-axis. I am unsure on which angle to take, alpha or beta. They are both angles of the positive side of the $x$ axis.
On the other hand, if a line $y=2$ was drawn then it would be clearer and would make angle B be the answer. However in this case I am unsure. A bit of clarification would be much appreciated!
It is solely matter of convention, in one case we talk of Right Hand System in the second of Left Hand System, note indeed that we need also to fix a z axes direction to define a clockwise and a counterclockwise direction for rotation.
In general, the angle between a line with direction $\mathbf v$ and a plane with normal $\mathbf n$ is $$\theta=\arcsin\left|\frac{\mathbf v \cdot\mathbf n}{\left|\mathbf v\right| \,\left|\mathbf n\right|} \right|.$$
Since the $xy-,$ $yz-, zx-$ planes have respective normals $\begin{pmatrix}0\\0\\1\end{pmatrix},\begin{pmatrix}1\\0\\0\end{pmatrix},\begin{pmatrix}0\\1\\0\end{pmatrix},$ as pointed out by Ted, your own answers are indeed correct.
P.S. The above formula has a similar derivation as yesterday's formula for the angle between two planes.
Best Answer
"Positive sense" is a direction (to the right here). That's different from "positive side". So probably $\beta$.
I say "probably" because you need the sense of the line, too. $\beta$ is the answer if you assume the line goes up to the left - a counterclockwise rotation from the $x$-axis. If the sense of the line is down to the right then $\alpha$ is the angle.
The question really is ambiguous. The best kind of response starts with "If by ... you mean ... then the answer is ...".