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Geometry and TrigonometryHardExterior angle of a triangle

Geometry and Trigonometry practice question

One exterior angle of a triangle measures 130°. One of the two interior angles not adjacent to it measures 45°. What is the measure of the other non-adjacent interior angle?

  1. A. 85°Correct
  2. B. 50°
  3. C. 95°
  4. D. 130°

Answer: A. 85°

An exterior angle equals the sum of the two interior angles that are not adjacent to it. So 130° = 45° + (other), giving 85°. (Check: the adjacent interior angle is 50°, and 50° + 45° + 85° = 180°.)

Why the other answers are wrong

B. 50°
50° is the interior angle ADJACENT to the exterior angle (180° − 130°). The question asks for a non-adjacent one.
C. 95°
95° comes from 180° − 130° + 45°, mixing the two relationships. The direct rule is exterior = sum of the two remote interior angles.
D. 130°
130° is the exterior angle itself. The remote interior angles are each smaller than it, since they add up to it.

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