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?



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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