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

The sum of the interior angles of a triangle is always 180 degrees, regardless of the type of triangle (whether it be scalene, isosceles, or equilateral). This fundamental property of triangles is a key concept in geometry and is derived from the fact that triangles can be formed and analyzed using parallel lines and other geometric principles.

To understand why the sum is specifically 180 degrees, consider a triangle drawn on a flat surface. If one angle is manipulated while keeping the other angles fixed, the total measure changes in a way that maintains the total at 180 degrees. This property also has applications in various proofs and problems in geometry, making it an important concept for students to grasp.

This rule does not apply to quadrilaterals or other polygons, which have different angle sum properties. For instance, a quadrilateral sums up to 360 degrees, which is double that of a triangle, illustrating the unique relationship triangle angles have within the framework of plane geometry.