What is the sum of the interior angles of any triangle in degrees?

• A. 120 degrees
• B. 360 degrees
• C. 180 degrees
• D. 90 degrees

Answer: (C)

In Euclidean geometry, the three interior angles of any triangle add up to a straight angle: 180 degrees. A clear way to see this is to draw a line through one vertex parallel to the opposite side; the other two interior angles become corresponding angles along that line, so together with the angle at the vertex they lie on a straight line and sum to 180 degrees. That’s why the total is 180 degrees.

This is why 180 degrees is the correct sum. The other totals don’t describe a triangle in the plane: 360 degrees would be a full rotation, and 90 or 120 degrees would contradict the requirement that the three interior angles total to a straight angle of 180 degrees.