What is the sum of the angles in a triangle?

The sum of the angles in a triangle is always 180 degrees, which is a fundamental property of triangles in Euclidean geometry. This relationship holds true for all types of triangles, whether they are scalene, isosceles, or equilateral.

To understand why the sum is 180 degrees, consider a triangle formed by three sides and three angles. When you draw a line parallel to one side of the triangle, the alternate interior angles created with the other two sides will equal the angles of the triangle. The total measure of these angles, because they encompass the entire internal space of the triangle, sums to precisely 180 degrees.

This property is essential for solving various geometry problems and provides the basis for more complex concepts in mathematics, including trigonometry and polygonal geometry.