What is the sum of the angles in a triangle?

The sum of the angles in a triangle is always 180 degrees. This is a fundamental property of triangles in Euclidean geometry. When you consider a triangle, it can be divided into two right triangles by drawing a line from one vertex perpendicular to the opposite side. The angles of the original triangle are the sum of the angles of these two right triangles, which add up to 90 degrees each, plus the vertex angle at the top, confirming that all three angles combined equal 180 degrees.

This property holds true for any type of triangle, whether it is scalene, isosceles, or equilateral. It is essential to grasp this concept not only for solving geometric problems but also as a building block for more advanced topics in mathematics, such as trigonometry and polygon properties. Understanding that the sum is consistently 180 degrees allows one to work effectively with various problems involving triangles and their properties.