The measure of an exterior angle of a triangle equals the sum of the measures of the two nonadjacent interior angles.

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Multiple Choice

The measure of an exterior angle of a triangle equals the sum of the measures of the two nonadjacent interior angles.

The exterior angle theorem says that an exterior angle of a triangle equals the sum of the two remote interior angles. Think of a triangle with interior angles A, B, and C. If you extend one side to create an exterior angle at a vertex, that exterior angle E together with the adjacent interior angle at that vertex form a straight line, so E + (the adjacent interior angle) = 180 degrees. Since the three interior angles sum to 180 degrees, A + B + C = 180, which means A + B = 180 − C. But E = 180 − (the adjacent interior angle) as well, so E = 180 − C. Therefore E = A + B, the sum of the two interior angles not adjacent to the exterior angle. A quick check: if the interior angles are 50°, 60°, and 70°, the exterior angle at the 70° corner is 110°, and indeed 50° + 60° = 110°. This relationship holds for any triangle, so the statement is true.

The exterior angle theorem says that an exterior angle of a triangle equals the sum of the two remote interior angles.

Think of a triangle with interior angles A, B, and C. If you extend one side to create an exterior angle at a vertex, that exterior angle E together with the adjacent interior angle at that vertex form a straight line, so E + (the adjacent interior angle) = 180 degrees. Since the three interior angles sum to 180 degrees, A + B + C = 180, which means A + B = 180 − C. But E = 180 − (the adjacent interior angle) as well, so E = 180 − C. Therefore E = A + B, the sum of the two interior angles not adjacent to the exterior angle.

A quick check: if the interior angles are 50°, 60°, and 70°, the exterior angle at the 70° corner is 110°, and indeed 50° + 60° = 110°. This relationship holds for any triangle, so the statement is true.

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