AB is a diameter of a circle with centre O. If C is any point on the circle such that BAC = 42º, then find the measure of BOC.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 84º.
In △ABC, ∠A + ∠B + ∠C = 180° [∵Angle sum property]
⇒ 42° + ∠B + 90° = 180° [∵Angle in a semi-circle is 90°]
⇒ ∠B = 180° - 90°- 42° = 48°
In △BOC, ∠OBC + ∠BOC + ∠BCO = 180°
⇒ 48° + 48° + ∠BOC = 180° [∵Angles opposite to equal sides are equal]
⇒ ∠BOC = 180° - 48° - 48° [ BO = CO = r]
∠BOC = 84°