Discussion

In triangle ABC, the bisectors of angle B and angle C meet at point O. If angle A = 70°, what is the measure of angle BOC?

Answer: C

In triangle ABC, Angle A + Angle B + Angle C = 180°. So, B + C = 180° - 70° = 110°.

The bisectors of B and C meet at O. In triangle BOC, the angles are Angle BOC, Angle OBC (which is B/2), and Angle OCB (which is C/2).

Angle BOC + B/2 + C/2 = 180°

Angle BOC + (B+C)/2 = 180°

Angle BOC + 110°/2 = 180°

Angle BOC + 55° = 180°

Angle BOC = 125°.

A standard formula for this is Angle BOC = 90° + (Angle A)/2 = 90 + 70/2 = 90 + 35 = 125°.

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