Angles

Intuition and core definition

An angle measures rotation between two rays sharing a vertex. Degree measure divides a full turn into $360^\circ$; a right angle is $90^\circ$, a straight angle $180^\circ$, and a reflex angle lies between $180^\circ$ and $360^\circ$. The length of drawn rays does not affect angle measure.

Notation, language, and conditions

$\angle ABC$ names the angle whose vertex is the middle letter $B$. A small square marks a right angle. Acute angles are between $0^\circ$ and $90^\circ$, obtuse between $90^\circ$ and $180^\circ$, and zero/full rotations require context. Angle measure may also use radians in trigonometry.

Why this idea matters

Angles measure rotation between rays, and their classification communicates size independently of how a diagram is drawn.

A dependable method

1. Identify the vertex and the two rays.
2. Name the angle with the vertex letter in the middle.
3. Estimate its class before measuring.
4. Align a protractor centre with the vertex and baseline with one ray; read the scale starting at zero on that ray.
5. Check that the numerical measure agrees with the visual class.

Worked example

Common mistakes