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 :
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]15°
[B]45°
[C]30°
[D]60°
15°
∠BCD = ∠DCA = 30°
∠DCE = 180°
∴ ∠ACE = 180° – 30° = 150°
AC = CE
∴ ∠CAE = ∠CEA = $latex \frac{30^{\circ}}{2}&s=1$ $latex = 15^{\circ}$
Hence option [A] is the right answer.