ABC is an equilateral triangle and CD is the internal bisector

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ABC is an equilateral triangle and CD is the internal bisector of ∠ C. If DC is produced to E such that AC = CE, then ∠ CAE is equal to

1. 45°
2. 75°
3. 30°
4. 15°

Correct Option: D

We draw a figure of an equilateral triangle ABC ,

∠ BCD = ∠ DCA = 30°
∠ DCE = 180°
∴ ∠ ACE = 180° – 30° = 150°
AC = CE
∴ ∠ CAE = ∠ CEA = (30° ÷ 2) = 15°