If a triangle has interior angles 30 degrees and 60 degrees, what is the measure of the exterior angle at the third vertex?

If a triangle has interior angles 30 degrees and 60 degrees, what is the measure of the exterior angle at the third vertex?

• A. 30 degrees
• B. 60 degrees
• C. 120 degrees
• D. 90 degrees

Answer: (D)

In a triangle, an exterior angle equals the sum of the two interior angles not at that vertex. Here, the two remote interior angles are 30 and 60, so the exterior angle at the third vertex is 30 + 60 = 90 degrees. Another way to see it: the third interior angle is 180 - (30 + 60) = 90 degrees, and the exterior angle adjacent to a 90-degree interior angle is supplementary, giving 180 - 90 = 90 degrees. Therefore, the exterior angle measures 90 degrees.

In a triangle, an exterior angle equals the sum of the two interior angles not at that vertex. Here, the two remote interior angles are 30 and 60, so the exterior angle at the third vertex is 30 + 60 = 90 degrees. Another way to see it: the third interior angle is 180 - (30 + 60) = 90 degrees, and the exterior angle adjacent to a 90-degree interior angle is supplementary, giving 180 - 90 = 90 degrees. Therefore, the exterior angle measures 90 degrees.