In any triangle ABC the internal bisector of ∠ABC and

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In any triangle ABC the internal bisector of ∠ABC and the external bisector of other base angle meet at point E. Then ∠BEC = ?

1. ∠A
2. 2∠A
3. 1 ∠A
  2
4. 1 ∠B
  2

Correct Option: C

According to question , we draw a figure of a triangle ABC in which the internal bisector of ∠ABC and the external bisector of other base angle meet at point E

As we know that , Exterior angle = Sum of two alternate angles
Exterior ∠ACD = ∠A + ∠B

⇒	1	∠ACD =	1	∠A +	1	∠B
	2		2		2

⇒∠ 2 = ∠ 1 +	1	∠A.........(i)
	2

In ∆ BCE,
∠ ECD = ∠1 + ∠E
⇒∠ 2 = ∠ 1 + ∠ E .........(ii)
From equations (i) and (ii),

∠1 +	1	∠A = ∠1 + ∠E
	2

⇒	1	∠A = ∠E
	2

⇒ ∠E =	1	∠A
	2