What is an Angle?

Geometry · Axiom Academy

Two rays, one shared corner, and a number that says how far one has turned from the other. An angle is an amount of turning An angle is formed by two rays that share a common endpoint called the vertex . We measure the opening between them in degrees (°) : a quarter turn is 90°, a half turn is 180°, and one full rotation all the way around is 360°. Watch one ray swing open from the other, and notice how a single number — the degree measure — captures exactly how wide the opening is. One ray stays put; the other sweeps open from 0° toward a full turn. The wedge between them is the angle, and the running degree readout tells you its size — and what we'd call it — at every instant. The bigger the opening, the bigger the angle — all the way around to 360°, a full rotation back to where it started. Open it yourself — and name what you make Drag the moving ray (or the slider) to set any angle from 0° to 360°. As you go, the angle is classified for you. Try to feel out the exact boundaries: where acute becomes right, where obtuse becomes straight, where straight rolls over into reflex. Same vertex, same starting ray — only the opening changes, and that single number decides what kind of angle it is. Two angles that finish each other off Angles often come in pairs that add to a special total. Drag the divider to split a fixed total between two angles, and watch one shrink as the other grows — their measures always sum to the same number.

This is the written version of the interactive lesson above. See the full Geometry course.