Question

Points A, B, C are on the circle such that m(arc ABC) = 120°. Find measure of angle

ABC.​

Answer 1

Answer:

(A) Equilateral triangle.

m(arc AB) + m(arc BC) + m(arc AC) = 360° [Measure of a circle is 360°]

∴ 120° + 120° + m (arc AC) = 360°

∴ m(arc AC) = 120°

∴ arc AB = arc BC = arc AC.

∴ seg AB ≅ seg BC ≅ seg AC [Corresponding chords of congruents arcs of a circle are congruent]

∴ ∆ABC is an equilateral triangle.