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In triangle ABC with sides a, b, c opposite to angles A, B, C respectively, it is given that a/(b+c) + b/(c+a) = 3/(a+b+c). Find the measure of angle C.

1. 30 deg
2. 45 deg
3. 60 deg
4. 90 deg

Correct answer: 60 deg

Solution

Substituting a = b, the equation gives 2/(1+c) = 3/(2+c), leading to c = a = b, confirming equilateral with C = 60 deg. Algebraic manipulation of the general equation yields the cosine rule condition cos(C) = 1/2, so C = 60 deg.

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