What is the relationship of exterior angles to the interior angles of a triangle?

The correct relationship is that an exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. This relationship is a fundamental property of triangles that arises from the definition of exterior angles.

When you extend one side of a triangle, the exterior angle formed at that vertex is supplementary to the adjacent interior angle. This means that if you know one of the interior angles and the exterior angle, the sum of these two angles equals 180 degrees. Therefore, the exterior angle must also include the other non-adjacent interior angle to maintain this balance.

Thus, if you take the external angle and subtract the interior angle that is adjacent to it, you are left with the sum of the two angles that are not adjacent to it, which reinforces this relationship. This property is very useful in solving problems related to triangles and can help in deriving other important geometric principles.

Options indicating that the exterior angle is equal to half of an interior angle or multiplying an interior angle by two do not support the established rule about exterior and interior angles. The choice stating that an exterior angle is equal to the sum of all three interior angles misunderstands the triangle angle sum theorem, which states that the sum of all angles in any triangle is