ACT-Style: Circle and Inscribed Angle

ACT Math · Axiom Academy

EXAMPLE ACT-Style: Circle and Inscribed Angle Finding an inscribed angle from a central angle, the way it actually shows up on the test In a circle with center O , the central angle . Point C lies on the major arc AB . What is the measure of the inscribed angle ? An inscribed angle is a two-step problem: first pin down which arc it opens onto, then halve that arc. The ACT's wrong answers are built from the specific slips that happen along the way. Central angle = its arc: means the minor arc AB is also . An inscribed angle is HALF its intercepted arc: , not (that trap forgets the ). Which arc matters: a vertex on the MAJOR arc opens onto the MINOR arc. Had C sat on the minor arc, would open onto the major arc ( ), giving — choice C, the classic distractor. On the ACT, circle-angle questions are rarely wrong because of hard arithmetic — they're wrong because the vertex's arc gets misidentified or the gets dropped. Name the intercepted arc first, then halve it.

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