An angle is formed by two rays sharing a common endpoint (the vertex). Angles are measured in degrees, from 0 to 360. They are classified by measure: acute (0-90), right (exactly 90), obtuse (90-180), and straight (exactly 180). The Angle Addition Postulate states that if ray BD is in the interior of angle ABC, then the measures add. Understanding angle classification is prerequisite to virtually every theorem in geometry.
Use a protractor to measure physical angles first. Classify angles by sight, then verify with measurement. Introduce notation (angle symbol, three-letter naming with vertex in the middle). Practice the Angle Addition Postulate with diagrams where angles are subdivided.
You have been working with points, lines, and planes as the primitives of geometry. An angle arises naturally the moment two rays share a common endpoint: that shared point is the vertex, and the opening between the rays is the angle. Angles appear everywhere in geometry — in triangles, parallel-line diagrams, circles, and polygons — so developing precise vocabulary for them now pays off immediately in every subsequent topic.
Angles are measured in degrees, where a full rotation is 360°. The classifications — acute (0°–90°), right (exactly 90°), obtuse (90°–180°), and straight (exactly 180°) — are not arbitrary labels but reflect geometric distinctions with real consequences. A right angle signals perpendicularity, which is the foundation of the Pythagorean theorem and coordinate geometry. A straight angle is just a straight line looked at from one end. Memorizing the classification thresholds is less important than understanding what they represent.
One of the most important misconceptions to correct early: the measure of an angle has nothing to do with the length of its rays. An angle of 45° between two short rays is identical in measure to a 45° angle between two very long rays. Angles measure rotation, not length. If you always think "how much would I have to rotate one ray to land on the other?", the measure follows directly from that rotation — ray length is irrelevant.
The Angle Addition Postulate provides the key tool for working with angles in diagrams: if a ray lies inside an angle, the two sub-angles it creates add to give the whole. Written symbolically: if BD is in the interior of ∠ABC, then m∠ABC = m∠ABD + m∠DBC. This looks simple, but it is the foundation for every geometric argument that involves breaking apart or combining angles — from proving triangle angle sums to analyzing parallel-line relationships. Practice identifying when a ray subdivides an angle in a figure and applying the postulate fluently, because it appears constantly in proofs.