Multiple choice

In (\triangle ABC), the sides AB and AC are produced to points E and D respectively. OB and OC are the external bisectors of (\angle EBC) and (\angle DCB) respectively. They meet at point O. If (\angle BAC = 54^{\circ}), then find (\angle BOC).

  1. $44^{\circ}$
  2. $55^{\circ}$
  3. $63^{\circ}$
  4. $78^{\circ}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In triangle ABC, ∠BAC = 54°. For external angle bisectors meeting at O: ∠BOC = 90° - ∠A/2 = 90° - 54°/2 = 90° - 27° = 63°. Option C is correct.

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