If OD is perpendicular to AB, and ∠DOC = 30°, find ∠BOC - ∠AOC.


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Answer:

60°

Step by Step Explanation:
  1. According to the question, ∠DOC = 30° and OD is perpendicular to AB.
    Therefore, ∠AOD = 90° and ∠BOD = 90°.
  2. Also, ∠DOC + ∠AOC = ∠AOD
    ⇒ 30° + ∠AOC = 90° (As, ∠AOD = 90° and ∠DOC = 30°)
    ⇒ ∠AOC = 90° - 30°
    ⇒ ∠AOC = 60°
  3. Now, ∠BOC - ∠AOC = ∠BOD + ∠DOC - ∠AOC (As, ∠BOC = ∠BOD + ∠DOC)
    = 90° + 30° - 60° (As, ∠BOD = 90°, ∠DOC = 30° and ∠AOC = 60°)
    = 60°
  4. Therefore, ∠BOC - ∠AOC = 60°

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