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      Question

      In the given figure, O is the centre of the circle, AE

      is the diameter and ∠AOC = 100°.   The value of ∠CDE + ∠CEA is: 
      A 90° Correct Answer Incorrect Answer
      B 80° Correct Answer Incorrect Answer
      C 60° Correct Answer Incorrect Answer
      D 100° Correct Answer Incorrect Answer

      Solution

      For ∠CDE: Consider chord CE ∠COE is the angle subtended by the chord CE at centre and  ∠CDE is the angle subtended by the same chord at the circumference. So, ∠CDE = 1/2 × ∠COE = 1/2 × 80 = 40°  For ∠CEA: Consider chord AC ∠AOC is the angle subtended by the chord AC at centre and ∠CEA is the angle subtended by the same chord at the circumference. So, ∠CEA = 1/2 × ∠AOC = 1/2 × 100 = 50°  Thus, ∠CDE + ∠CEA = 40 + 50 = 90° 

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