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Question

In a △ABC, if 2∠A = 3∠B = 6∠C, then th s measure of the smallest angle is
(a) 90°
(b) 60°
(c) 40°
(d) 30°

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Solution

We have
2∠A = 3∠B = 6∠C
3B=2A and 6C=2AB=23A and C=26A=13ANow, A+B+C=180° [Angle sum property of triangle]A+23A+13A=180°3A+2A+A=180°×36A=540°A=90°

∴ Smallest angle = C=13A=13×90°=30°
Hence, the correct answer is option (d).

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