In the given figure, ΔABC and ΔDBC are inscribed in a circle such that ∠BAC = 60° and ∠DBC = 50°. Then, ∠BCD = ?
Given: Two triangles ΔABC and ΔBCD, ∠BAC = 60° and ∠DBC = 50°
We know that ∠BAC = ∠BDC = 60° ( angles in the same segment drawn from same chord are
equal).
Now consider ΔBCD
By angle sum property
∠DBC + ∠BDC + ∠BCD = 180°
50° + 60° + ∠BCD = 180°
∠BCD = 180° – 50° – 60°
∠BCD = 70°
∴ ∠BCD = 70°