Are there any more terms to describe angles? My textbook gives the following list:
Null angle: $\theta =0^\circ$
Acute angle: $0^\circ \le \theta \le 90^\circ$
Right angle: $\theta =90^\circ$
Obtuse angle: $90^\circ \le \theta \le 180^\circ$
Straight angle: $\theta =180^\circ$
Ordinary angle: $0^\circ \le \theta \le 180^\circ$
Reflex angle: $180^\circ \le \theta \le 360^\circ$
Full angle: $\theta =360^\circ$
Are there any terms for say:
$180^\circ \le \theta \le 270^\circ$
$270^\circ \le \theta \le 360^\circ$
$\theta =270^\circ$
$\theta \ge 360^\circ$
 A: All these depend on definition.
I like the following definition.
Angle it's an union of two rays, which have a common vertex and don't placed on the same line.
Any angle has a measure, which goes between $0^{\circ}$ and $180^{\circ},$ which we can get by the protractor.
About the rest we can say as generalized angles.
Now, let $\theta$ be a measure of some angle.
Thus, for $0^{\circ}<\theta<90^{\circ}$ we say about an acute angle,
for $\theta=90^{\circ}$ we say about a right angle,
for $90^{\circ}<\theta<180^{\circ}$ we say about an obtuse angle and
For generalized angle we can define a measure $\theta$ for which $\theta\leq0^{\circ}$ or $\theta\geq180^{\circ}$.
A: While maybe slightly out of the scope of the question, you can identify angles with the inverse trigonometric functions. For instance, we can say the angle $270^\circ$ is $\sin^{-1}(-1)$ (where the negative one is used to indicate the inverse function, not a reciprocal).
This also has the advantage of being able to describe ranges of angles, for instance $0^\circ\leq\theta \leq 180^\circ$ can be viewed as the preimage under $\cos^{-1}(x)$ for $x$ in $[-1,1]$, or succinctly $\cos^{-1}([-1,1])$.
Again, I admit these aren't quite "terms" in the spirit of the question but this idea can be used to describe some of the quantities you didn't find a name for!
A: A land surveying azimuth direction is often a clockwise angle from North between 0 and 360 degrees.
(Mathematical slope is a counterclockwise angle from a horizontal that is pointing to the right.)
Land surveying, and often legal descriptions, also have four-quadrant directions in degrees.
The first quadrant is a clockwise angle from North between 0 and 90 and written as NangleE .
The second quadrant is a counterclockwise angle from South between 0 and 90 and written as SangleE.
The third quadrant is a clockwise angle from South between 0 and 90 and written as SangleW.
The fourth quadrant is a counterclockwise angle from North between 0 and 90 and written as NangleW.
