In the given figure, ΔABC and ΔDBC are inscribed in a circle such that ∠BAC = 60° and ∠DBC = 50°. Then, ∠BCD = ?

Question

In the given figure, ΔABC and ΔDBC are inscribed in a circle such that ∠ BAC = 60 ° and ∠ DBC = 50 ° . Then, ∠ BCD = ?

Philoid · Accepted Answer

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°