In the given figure, equilateral ΔABC is inscribed in a circle and ABDC is a quadrilateral, as shown. Then, ∠BDC = ?

Question

In the given figure, equilateral ΔABC is inscribed in a circle and ABDC is a quadrilateral, as shown. Then, ∠ BDC = ?

Philoid · Accepted Answer

Given: ΔABS is equilateral

In ΔABC

∠BAC = 60° (All angles in equilateral triangle are equal to 60°)

We know that,

In a cyclic quadrilateral opposite angles are supplementary

∴ ∠BAC + ∠BDC = 180°

60° + ∠BDC = 180°

∠BDC = 180° – 60° = 120°

∴ ∠BDC = 120°