Angles — Vertical, Supplementary, Complementary

ACT Math · Axiom Academy

LESSON Angles: Vertical, Supplementary, Complementary The essential angle relationships behind nearly every geometry question on the ACT — seen as the motion that makes each one true. 1. Complementary & Supplementary Angles Two of the most common relationships are defined purely by what a pair of angles adds up to . Complementary angles fill a right angle; supplementary angles fill a straight line. Watch the split ray slide: one part grows exactly as much as the other shrinks, so the total never changes. Complementary — the pair fills a right angle Supplementary — the pair fills a straight line When two lines cross, they form four angles. The pair sitting opposite each other — sharing only the crossing point — are called vertical angles. As the animation rotates the crossing lines, watch the two opposite angles stay locked to the same measure, while each neighboring pair keeps adding to 180°. The two angles across the intersection from each other. These are the vertical pair. Vertical angles are ALWAYS equal, no matter how the lines are tilted. Any two adjacent angles form a straight line, so they are supplementary (sum 180°). Each vertical angle equals 180° minus the same neighbor — so they must equal each other. If one angle where two lines cross is , the angle directly opposite is also — and each neighbor is . 3. Parallel Lines and Transversals

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