An exterior angle of a triangle equals the sum of which interior angles?

• A. The two interior opposite angles
• B. The adjacent interior angle
• C. All three interior angles
• D. None of the interior angles

Answer: (A)

When a triangle’s side is extended, the outside angle formed is called an exterior angle. This exterior angle and the interior angle at the same vertex form a straight line, so they are a linear pair and sum to 180 degrees. Since the three interior angles of a triangle also sum to 180 degrees, the exterior angle must equal 180 minus the measure of the adjacent interior angle. That ends up being the sum of the other two interior angles—the ones not adjacent to the exterior angle. So the exterior angle equals the sum of the two interior opposite angles.

It isn’t equal to the adjacent interior angle, because that would contradict the 180-degree straight line rule. It isn’t equal to all three interior angles, since their sum is 180 and the exterior angle is a single angle formed outside.