Multiple choice

In ∆ABC, sides AB and AC are produced to point D and E respectively. The angle bisectors of ∠CBD and ∠BCE meets at O. If ∠BOC = 69°, then find the value of ∠A?

  1. 22°

  2. 44°

  3. 21°

  4. 42°
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D Correct answer
Explanation

When AB and AC are produced, O is intersection of external angle bisectors of ∠CBD and ∠BCE. Using exterior angle bisector theorem: ∠BOC = 90° - (∠A/2). Given ∠BOC = 69°, we have 69° = 90° - (∠A/2), so ∠A/2 = 21° and ∠A = 42°. This property relates intersection of external bisectors to the original vertex angle.

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