As shown in the figure, from runway 1 airplanes must turn 120° to the right onto runway 2 or 135° to the left onto runway 3.

Note: Figure is not drawn to scale.
Which of the following does NOT indicate a complete turn from one runway to another?

55°

Explanation

The key to this problem is in determining the interior angles of the various triangles formed by the runways. The interior angle formed by the 120° turn from runway 1 to 2 is 60° (a 180° turn would reverse the airplane’s direction). Similarly, the interior angle formed by the 135° turn from runway 1 to 3 is 45° (180° – 135°). Two right-triangle “angle triplets” emerge: a 45°-45°-90° triplet and a 30°-60°-90° triplet, as shown in the figure. Since the sum of any triangle’s interior angles is 180°, the remaining angles can also be determined.The only angle measure listed among the answer choices that does not appear in the figure is 55°.

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