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      Question

      In a circle AB is diameter and points C and D are on

      the circumference such that ∠ CAD = 40° and ∠ CBA = 60°. What is the value of ∠ ACD?
      A 20° Correct Answer Incorrect Answer
      B 30° Correct Answer Incorrect Answer
      C 40° Correct Answer Incorrect Answer
      D 50° Correct Answer Incorrect Answer

      Solution

      According to figure above, ∠ CAD and ∠ CBD subtend the same arc DC on the circumference. ⇒∠ CAD = ∠ CBD = 40° Also, ∠ DBA = ∠ CBA - ∠ CBD = 60 - 40 = 20°. Now ∠ DBA and ∠ ACD subtend the same arc DA on the circumference of the circle. ⇒∠ ACD = ∠ DBA = 20°.

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