Angles and Their Measure

Pre-Calculus · Axiom Academy

LESSON Angles and Their Measure An angle is a rotation — where it stops, which way it turned, and which angles secretly share the same finish line. Pin one end of a ray at a point — the vertex — and let it start lying along a fixed initial side . Now rotate it. Where it stops is the terminal side , and the amount of turn between them is the angle . Watch the ray sweep open below. To compare angles we agree on a starting setup. An angle is in standard position when its vertex sits at the origin and its initial side runs along the positive x-axis . Then the terminal side falls into one of four quadrants, and the same angle always looks the same. Terminal side between and — here and . Between and — the terminal side points up and to the left. Between and — down and to the left. For example lands here. Between and — down and to the right. Rotation has a direction, and that direction carries the sign . Turning counterclockwise makes the angle positive ; turning clockwise makes it negative . Below, both rays open to the same opening, but one swept and the other — and they finish on different terminal sides. Against the clock. sweeps up into Quadrant II. With the clock. sweeps down into Quadrant III.

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