In the given diagram, chords AC and BC are equal. If ∠ACD = 120°, then ∠AEC is:
30°
60°
90°
120°
Circles
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Question

In the given diagram, chords AC and BC are equal. If ∠ACD = 120°, then ∠AEC is: 1. 30° 2. 60° 3. 90° 4. 120°

KnowledgeBoat · Accepted Answer

From figure, ∠ACD and ∠ACB forms linear pairs [BD is a straight line]. ⇒ ∠ACD + ∠ACB = 180° ⇒ 120° + ∠ACB = 180° ⇒ ∠ACB = 180° - 120° ⇒ ∠ACB = 60°. In ΔABC, ⇒ BC = AC [Given] ⇒ ∠ABC = ∠BAC = x° (let) [Angles opposite to equal sides in triangle are equal] According to angle sum property in ΔABC, ⇒ ∠ACB + ∠ABC + ∠BAC = 180° ⇒ 60° + x° + x° = 180° ⇒ 2x° = 180° - 60° ⇒ 2x° = 120° ⇒ x° = = 60°. From figure, ABCE is cyclic quadrilateral. We know that, Opposite angles of cyclic quadrilateral are supplementary. ⇒ ∠ABC + ∠AEC = 180° ⇒ 60° + ∠AEC = 180° ⇒ ∠AEC = 180° - 60° ⇒ ∠AEC = 120°. Hence, option 4 is the correct option.

Mathematics

In the given diagram, chords AC and BC are equal. If ∠ACD = 120°, then ∠AEC is:
30°
60°
90°
120°

Circles

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90°
120°

The equation of the line passing through origin and parallel to the line 3x + 4y + 7 = 0 is:
3x + 4y + 5 = 0
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