acute, right, obtuse, straight and reflex angles

Angles come in a natural order of openness, from a barely-cracked door to one swung almost all the way back. Sorting angles by how wide they are gives five everyday names that you will meet constantly: acute, right, obtuse, straight, and reflex.

Measured in degrees, the bands are: an acute angle is greater than 0° and less than 90° (a sharp, narrow corner); a right angle is exactly 90° (a perfect square corner, marked with a small square symbol); an obtuse angle is greater than 90° but less than 180° (open wider than a square corner); a straight angle is exactly 180° (the two sides form a straight line, opposite rays); and a reflex angle is greater than 180° and less than 360° (the 'outside' angle, more than a half-turn). A full angle of exactly 360° is sometimes added as a sixth.

These names are pure size labels, but they carry weight throughout geometry: a triangle is classified as acute, right, or obtuse by its largest angle; perpendicular lines meet at right angles; the right angle anchors the Pythagorean theorem and the whole of trigonometry. One trap to remember: any two rays bound both a smaller angle and a reflex angle that together total 360°, so the same drawing can be read as, say, an 80° angle or its 280° reflex partner — context tells you which is meant.