What is the sum of the interior angles of a triangle?

The sum of the interior angles of a triangle is always 180 degrees. This is a fundamental property in Euclidean geometry. Regardless of the type of triangle—whether it is scalene, isosceles, or equilateral—the total measure of the angles inside the triangle will always equal 180 degrees.

This can be derived from the properties of parallel lines and transversals, or through the use of a triangle's structure, such as by drawing a line parallel to one side of the triangle and utilizing the alternate interior angles formed.

The other options do not align with the established geometric principles: the sum of 90 degrees represents the total for the angles of a right triangle, while 270 and 360 degrees relate to different polygons, specifically quadrilaterals and circles respectively. Thus, the 180-degree sum is a critical concept that applies universally to all triangles in Euclidean space.