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.

20^o

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°