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?

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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