An angle is the amount of turn between two rays that start from the same point. That shared point is the vertex, and the two rays are the arms of the angle. The wider the opening between the arms, the bigger the angle.

We measure that turn in degrees, written with a little circle: ^\circ. One full spin all the way around — back to where you started — is 360°. From there, every other angle is a fraction of a full turn:

• a full turn is 360^\circ;
• a straight angle (a half turn) is 180^\circ;
• a right angle (a quarter turn) is 90^\circ — the square corner, marked with a small square instead of an arc.

Drag the slider to swing the second arm around the vertex. Watch the reading climb from a thin sliver, through the right angle and the straight angle, all the way to a full turn.

Naming angles by size

Once you can measure an angle, you can sort it into a family by how big it is:

• Acute — smaller than a right angle: less than 90^\circ.
• Right — exactly 90^\circ (the square corner).
• Obtuse — between 90^\circ and 180^\circ.
• Straight — exactly 180^\circ, a flat half turn.
• Reflex — bigger than a straight angle: more than 180^\circ (but less than a full 360^\circ).

Step through one of each below.