An equilateral triangle ABC is inscribed in a circle with centre O. D is a point on the minor are BC and ∠ CBD = 40°. Find the measure of ∠ BCD.
∠ABC = ∠ACB = ∠BAC = 60° [∵ ΔABC 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° ∴ The value of ∠BCD is 20°
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