Q34 of 141 Page 447

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

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°

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