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MHT CET202620 April 2026Evening ShiftMathematicsProperties of TrianglesActual

The angles of ABC are in A.P. and b : c = 3 : 2 then A =

Options

  1. A30^
  2. B90^
  3. C105^
  4. D75^

Correct answer

D. 75^

Step-by-step solution

Given angles A, B, C are in A.P. 2B = A + C Since A + B + C = 180^ , we have 3B = 180^ B = 60^ Using the sine rule, b B = c C Substituting the given ratio b c = 3 2 and B = 60^ : 3 2 = 60^ C 3 2 = 3 2 C C = 1 2 Since B = 60^ , C cannot be 135^ (as B + C = 195^ > 180^ ), so C = 45^ The sum of angles in a triangle is 180^ : A + B + C = 180^ A + 60^ + 45^ = 180^ A = 75^ Answer: 75^

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