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 of triangles in Euclidean geometry and holds true regardless of the type of triangle, whether it is acute, right, or obtuse. The reason this is the case can be understood by considering how a triangle can be formed and how the angles are related: if you draw a triangle and extend one of its sides, the exterior angle formed is equal to the sum of the two opposite interior angles. The geometry of the triangle ensures that adding all three interior angles will result in a total of 180 degrees.

Understanding this property is critical in solving various geometry problems and proofs, as it serves as a basis for further exploration into polygon angle sums and relationships between different shapes. This 180-degree rule for triangles is universally applicable in plane geometry and simplifies many calculations and constructions in both academic and practical applications.