Final answer:
The Triangle Sum Theorem states that the sum of a triangle's interior angles is 180 degrees. In contrast, the Exterior Angle Theorem says an exterior angle of a triangle equals the sum of the two non-adjacent interior angles. These theorems define crucial relationships between a triangle's angles, helping solve geometric problems.
Step-by-step explanation:
The Triangle Sum Theorem states that the sum of the three interior angles of a triangle is always 180 degrees. This fundamental property of triangles is crucial for understanding the geometry of any polygon.
On the other hand, the Exterior Angle Theorem asserts that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles. Essentially, this means that an exterior angle is equal to the sum of the opposite interior angles.
These two theorems relate to each other in the way they describe the relationships between the angles of a triangle. Understanding both principles allows one to solve various problems in geometry by providing a foundation about the nature of triangles and their angles.