In geometry, what is the sum of the interior angles of a triangle?

The sum of the interior angles of a triangle is established as 180 degrees through geometric principles. This can be understood by considering that a triangle can be divided into two right triangles by drawing a line from one vertex to the opposite side. Each right triangle has two angles that together sum to 90 degrees. Since there are two right triangles formed, plus the angle at the vertex, the sum becomes 90 degrees + 90 degrees = 180 degrees for the entire triangle.

This property is foundational in Euclidean geometry and holds true for all types of triangles, whether they are scalene, isosceles, or equilateral. Understanding this concept is crucial, as it can be applied in various geometric proofs and problem-solving scenarios.