Multiple choice

In △ABC, ∠A= 66∘.AB and AC are produced to points D and E, respectively. If the bisectors of angle CBD and angle BCE meet at the point O, then ∠BOC is equal to:

  1. 57∘

  2. 93

  3. 114∘

  4. 66∘
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A Correct answer
Explanation

∠CBD = 180° - ∠ABC and ∠BCE = 180° - ∠ACB (exterior angles). Since ∠A + ∠ABC + ∠ACB = 180° and ∠A = 66°, we have ∠ABC + ∠ACB = 114°. In quadrilateral BOC formed by bisectors: ∠BOC = 180° - (∠CBD/2 + ∠BCE/2) = 180° - (180° - ∠A)/2 = 180° - 114°/2 = 180° - 57° = 57°.

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