ABC is an equilateral triangle and CD is the internal bisector of ang C If DC is produced to E such ...........

Quantitative Aptitude ( CCS) Geometry

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

45°

75°

30°

15°

∠BCA = 60°
[? ΔPQR is an equilateral]

∠BCD = ∠DCA = 30°
[? CD is bisector of ∠C of an equilateral triangle]
∠DCE = 180°

∠ACE = 180° – 30° = 150°

∠CAE + ∠CEA = 180° – 150° = 30° ...(i)

Given, AC = CE

∴ ∠CEA = ∠CAE

From Eq. (i),

2∠CAE = 30°
∴ ∠CAE = 15°

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