AC is the diameter of a circumcircle of ∆ ABC. Chord

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AC is the diameter of a circumcircle of ∆ ABC. Chord ED is parallel to the diameter AC. If ∠CBE = 50°, then the measure of ∠DEC is

1. 50°
2. 90°
3. 60°
4. 40°

Correct Option: D

According to question , we draw a figure circle and chord ED is parallel to the diameter AC

∠CBE = 50°
∠BAC + ∠BCA = 90° [∵ ∠ABC = 90°]
∠ABE = 90° – 50° = 40°
∴ ∠ABE = ∠ACE = 40°
∴ ∠ACE = ∠DEC = 40°