What is the sum of the angles in a triangle?

The sum of the angles in a triangle is always 180 degrees. This fundamental property holds true for all types of triangles, regardless of their shape or size.

To understand this, consider that a triangle can be formed by connecting three points (the vertices) in a plane. When you draw the triangle, the internal angles created at each vertex combine to indicate how much "turn" is necessary to return back to the starting point after tracing the perimeter of the triangle. Since the angles in a triangle cover the full extent of turning needed to enclose the shape, they add up to form a complete angle of 180 degrees.

In various geometrical contexts, this rule is maintained. For example, when analyzing triangles in different geometries (like spherical or hyperbolic), the sum of angles can differ, but within Euclidean geometry, which encompasses the vast majority of practical applications, the answer remains consistently at 180 degrees.

This property can also be proven using various methods, including the use of parallel lines and transversals, thereby reinforcing its validity across numerous geometrical proofs and theorems.