There are two jobs here. First, classify an angle — say what type it is just from its size. Second, name an angle correctly. Both are quick once you know the rules.
Classify by Size
Every angle gets a name based on how open it is. Learn these five and you've got the lot:
Acute — less than 90°, a sharp little angle. Right — exactly 90°, the corner of a page (this is the one marked with the little square). Obtuse — between 90° and 180°, wider than a right angle but not yet a straight line. Straight — exactly 180°, the two arms make one straight line. Reflex — more than 180° (and less than 360°), the big way round.
Name It with ∠ and Three Letters
To name an angle you write ∠ then three points, with the vertex in the middle. If the corner is at B and the arms reach out to A and C, the angle is ∠ABC (and ∠CBA is the same angle — just read the other way). The two outside letters can swap; the middle one can't.
A Worked One
Say a diagram shows a corner at point Q, with one arm going to P and the other to R, and you measure the opening as 130°. Job one: 130° is between 90° and 180°, so it's an obtuse angle. Job two: vertex Q goes in the middle, so it's ∠PQR. Put it together: ∠PQR is an obtuse angle of 130°.
When Two Letters Is Enough — and When It Isn't
You'll sometimes see an angle written with just one letter, like ∠B, when there's only one angle at that point and there's no chance of confusion. But the moment several angles share a vertex, you must use all three letters so it's crystal clear which one you mean. When in doubt, use three.