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The three angles of a triangle are in arithmetic progression and the greatest is twice the least. The angles are:

Competition practiceTrigonometry
  • A30°, 60°, 90°
  • B45°, 60°, 75°
  • C40°, 60°, 80°
  • D20°, 60°, 100°

Step-by-Step Solution

In three terms in arithmetic progression the middle one is the average, so it is 180°/3 = 60° and the angles are 60° − , 60°, 60° + . The condition 60° + (60° − d) gives °, so ° and the angles are 40°, 60°, 80° — and indeed 80° = °. Each of the other lists is also an arithmetic progression summing to 180°, but there the greatest is three times, one and two-thirds times, and five times the least respectively.
Answer: C) 40°, 60°, 80°

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