Question

In the given diagram, chords AC and BC are equal. If ∠ACD = 120°, then ∠AEC is ______.

Options

• 30°

• 60°

• 90°

• 120°

Answer 1

In the given diagram, chords AC and BC are equal. If ∠ACD = 120°, then ∠AEC is 120°.

Explanation:

∠ACB + ∠ACD = 180° [linear pair]

∠ACB = 180° − ∠ACD

∠ACB = 180° − 120° = 60°

∠C = 60°

In ΔABC,

By the angle sum property of a triangle

∠A + ∠B + ∠C = 180°

∠A = ∠В    ...[Opposite angles are equal if opposite sides are equal]

∠A = x and ∠B = x

x + x + 60° = 180°

2x + 60° = 180°

2x = 120°

x = 60°

∠ABC = 60°

Opposite angles of a cyclic quadrilateral are equal to 180°.

∠ABC + ∠AEC = 180°

∠AEC = 180° – 60° = 120°