Let ABC be a triangle. angle A: angle B: angle C = 1: 2: 6.
Let x be the coefficient of proportionality, then angle A = x, angle B = 2x, angle C = 6x.
angle A + angle B + angle C = 180 degrees;
x + 2x + 6x = 180;
9x = 180;
x = 180/9;
x = 20.
Angle A = x = 20 degrees, angle B = 2x = 2 * 20 = 40 degrees, angle C = 6x = 6 * 20 = 120 degrees.
Since the angle C is more than 90 degrees, the ABC triangle is obtuse.
Answer: ABC is an obtuse triangle.
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