An equilateral triangle ABC is inscribed in a circle with centre O. D is a point on the mirror are BC and ∠CBD = 40°. Find the measure of ∠BCD.
Answer & explanation
Correct answer: option 3
We know that,
The sum of the opposite angles of a cyclic quadrilateral = 180°
The sum of all three angles of a triangle = 180°
We have,
∠CBD = 40º
∠ABC = ∠ACB = ∠BAC = 60°
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°