Lines and Angles

GRE Quantitative · Axiom Academy

The vocabulary and theorems behind every angle diagram you'll see — angle types, complementary pairs, parallel lines cut by a transversal, and the triangle angle-sum. 1. Angle Basics, Complementary & Supplementary An angle is formed by two rays that share a common endpoint, the vertex . Angles are measured in degrees , with a full rotation equal to 360°. By size, every angle falls into one of five families: — a flat line through the vertex. Two angles that share a ray can have a fixed-sum relationship no matter how either one is drawn: Complementary angles sum to 90° Supplementary angles sum to 180° Example — reading off both partners If one angle measures 35°, its complement is , and its supplement is . Another quick check: if two angles are complementary and one is 62°, the other is . 2. Vertical Angles & Parallel Lines Cut by a Transversal First, one more free relationship: when two lines cross , the angles directly opposite each other at the crossing are vertical angles , and vertical angles are always equal . You'll see this rule again in a moment — it's exactly what makes two of the four transversal relationships below hold. Same position at each intersection (e.g. both upper-right). Equal. Between the parallel lines, opposite sides of the transversal. Equal. Outside the parallel lines, opposite sides of the transversal. Equal. Between the parallel lines, same side of the transversal. Supplementary (sum to 180°) — not equal.

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