Q46
ArithmeticGeometry & Mensuration
The external bisectors of ∠ABC and ∠ACB of ΔABC meet at O. ∠BAC = 70°, value of ∠BOC = ?
- a.45°
- b.55°
- c.65°
- d.75°
Answer: (B) 55°
Where the external bisectors of B and C meet, $\angle BOC = 90^\circ - \frac{1}{2}\angle A$. With $\angle A = 70^\circ$ this is $90^\circ - 35^\circ = 55^\circ$. 125° would be the result for internal bisectors, and 45°, 65° and 75° do not fit the formula.