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Question

In the given figure, O is the centre of a circle and OAB = 50°. Then, ∠BOD = ?
(a) 130°

(b) 50°
(c) 100°
(d) 80°


Solution

(c) 100°
OA = OB  (Radii of a circle)
∠OBA = ∠OAB = 50°
In
Δ OAB, we have:
∠ OAB + ∠OBA + ∠AOB = 180°    (Angle sum property of a triangle)
50° + 50° + ∠AOB = 180°
∠AOB = (180° - 100°) = 80°
Since ∠AOB + ∠BOD = 180°
  (Linear pair)
∠BOD = (180° - 80°) = 100°

Mathematics
RS Aggarwal (2017)
Standard IX

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