In a triangle ABC, if 2\angle A=3\angle B=6\angle C, then what is \angle A+\angle C equal to?
- A. 90^{\circ}
- B. 120^{\circ} ✓
- C. 135^{\circ}
- D. 150^{\circ}
Correct Answer: B. 120^{\circ}
Explanation
Let 2\angle A = 3\angle B = 6\angle C = k. Then \angle A = \frac{k}{2}, \angle B = \frac{k}{3}, \angle C = \frac{k}{6}. Since sum of angles is 180^\circ, we have \frac{k}{2} + \frac{k}{3} + \frac{k}{6} = 180^\circ \Rightarrow k = 180^\circ. Therefore, \angle A = 90^\circ and \angle C = 30^\circ. The sum \angle A + \angle C = 90^\circ + 30^\circ = 120^\circ.
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