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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
Answer & Solution
Correct Answer:
Option
D
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°
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°
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