What is the sum of the angles in any triangle?

The sum of the angles in any triangle is always 180 degrees. This is a fundamental property of triangles in Euclidean geometry, which is the geometry of flat surfaces. Regardless of the type of triangle—whether it is scalene, isosceles, or equilateral—the internal angles always add up to this value.

This principle can be demonstrated using various methods, such as drawing a line parallel to one side of the triangle through the vertex opposite that side. The angles formed will illustrate that the angles inside the triangle correspond to exterior angles, leading to the conclusion that they must sum to 180 degrees.

This property is foundational in understanding not just triangles but also plays a significant role in more complex geometric relationships and proofs.