O is the centre of a circle, and A is a point on a major arc BC of the circle. ∠BOC and ∠BAC are the angles made by the minor arc BC on the centre and circumference, respectively. If ∠ABO = 40° and ∠ACO = 30°, then find ∠BOC.
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 140º.
Given that
∠ABO = 40° and ∠ACO = 30°,
In a circle, the angle at the centre is double the angle at the circumference
∠ABO = ∠OAB = 40º (opposite angles of equal sides are equal)
Similarly, ∠ACO = ∠OAC = 30°
So, ∠BAC = 40º + 30° = 70º
Hence, ∠BOC = 2 × ∠BAC = 2 × 70º = 140º