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Solution


Given:
    • We are given that a, b and c are the interior angles of a triangle ABC
    • a, b and c are integers

To find:
    • The number of possible values of a – b + c, which are < 0

Approach and Working:
Since, a, b and c, are interior angles of a triangle, we can say that,
    • a + b + c = \(180^o\)
    o Implies, a + c = 180 – b
    • Substituting this in the expression, a – b + c, we get,
    o a – b + c = (a + c) – b = (180 – b ) – b = 180 – 2b

For the value of 180 – 2b to be < 0
    • 2b > 180
    • b > 90

And, the maximum value that ‘b’ can take is \(178^o\), since, the minimum value of a and c are \(1^o\) each.
    • Thus, 91 ≤ b ≤ 178

Therefore, the total number of values that b can take is 88

Hence the correct answer is Option A.

Answer: A

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