With the usual notation, in ΔABC, if ∠A + ∠B = 120°, a = √3 + 1 and b = √3, then the ratio ∠A : ∠B, is:<p></p>

A + B = 120°
tan(A-B)/2 = (a-b)/(a+b)
cot(C/2) = (√3+1 - √3)/(√3+1 + √3) = 1/(2√3)
cot(30°) = √3
cot(C/2) = 1/2√3 * √3 = 1/2
(A-B)/2 = 45° ⇒ A - B = 90°
A + B = 120°

2A = 210°
A = 105°
B = 15°
∠A : ∠B = 7:1

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Question:

With the usual notation, in ΔABC, if ∠A + ∠B = 120°, a = √3 + 1 and b = √3, then the ratio ∠A : ∠B, is:

Solution: