In the given figure, AOB is a diameter and ABCD is a cyclic quadrilateral. If ∠ADC = 120°, then ∠BAC = ?

Question

In the given figure, AOB is a diameter and ABCD is a cyclic quadrilateral. If ∠ ADC = 120°, then ∠ BAC = ?

Philoid · Accepted Answer

Given: ABCD is cyclic quadrilateral and ∠ADC = 120°

Here,

∠ADC + ∠ABC = 180° (opposite angles in cyclic quadrilateral are supplementary)

120° + ∠ABC = 180°

∠ABC = 180° – 120°

∠ABC = 60°

Here,

∠ACB = 90° (angle in semicircle)

Now, consider ΔABC

By angle sum property

∠BAC + ∠ABC + ∠ACB = 180°

∠BAC + 60° + 90° = 180°

∠BAC = 180° – 60° – 90°

∠BAC = 30°