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

A. 45°

B. 75°

C. 30°

D. 15°

Answer: Option D

Solution(By Examveda Team)

According to question,
Given : ABC is an equilateral triangle CD is the angle bisector of ∠C

AC = CE
∴ ∠CAE = ∠CEA
   ∠ACD = 30°
∴ ∠ECA = 180° - 30°
   ∠ECA = 150°
In ΔCAE
   ∠CAE + ∠CEA + ∠ECA = 180°
∴ 2∠CAE = 180° - 150°
   2∠CAE = 30°
   ∠CAE = 15°