Are there any more terms to describe angles?

Question

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:

$180^\circ \le \theta \le 270^\circ$

$270^\circ \le \theta \le 360^\circ$

$\theta =270^\circ$

$\theta \ge 360^\circ$

Answer 1

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 $\theta\geq180^{\circ}$.

Answer 2

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.

Answer 3

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!