ABC is an equilateral triangle inscribed in a circle. 'D' is any point on the minor arc BC.Find the measure of ∠BDC.
Show answer & explanation
Correct answer: B
Explanation
ABC is an equilateral triangle; therefore,
∠A = ∠B = ∠C = 60°
An angle inscribed in a circle is equal to half the measure of its corresponding arc.
Thus, the central angle of minor arc BC = 2 × 60° = 120°
Therefore, the measure of major arc BC = 360° − 120° = 240°
Since D lies on minor arc BC, ∠BDC will be subtended by major arc BC.
Thus, ∠BDC = 240° / 2 = 120°