An equilateral triangle ABC is inscribed in a cicle with centre O. D is a point on the minor are BC and ∠CBD = 40°. Find the measure of ∠BCD.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 20°
ABC is an equilateral triangle and ∠CBD = 40°
∠ABC = ∠ACB = ∠BAC = 60° [ Because tri(ABC) is an equilateral triangle]
Also, ∠BAC + ∠BDC = 180°
=60° + ∠BDC = 180°
∠BDC = 180° - 60° = 120°
Also, ∠CBD + ∠BDC + ∠BCD = 180°
=40° + 120° + BCD = 180°
∠BCD = 180° - 40° - 120° = 20°
Therefore, The value of ∠BCD is 20°