How many degrees are in the sum of the interior angles of a triangle?

The sum of the interior angles of a triangle is 180 degrees. This is a fundamental property of triangles in Euclidean geometry.

To understand why this is the case, consider a triangle with three angles: let's denote them as angle A, angle B, and angle C. If you were to draw a line parallel to one side of the triangle that intersects the other two sides, the angles formed at this intersection can be shown to relate directly to the angles within the triangle. More specifically, the alternate interior angles created by this parallel line will be equal to angle A and angle B, and the angle formed on the outside will be equal to angle C. The total measure of these angles equals 180 degrees because they form a straight line.

This property holds true for every triangle regardless of its type (scalene, isosceles, or equilateral), making 180 degrees the sum of the interior angles for all triangles in a flat plane. Understanding this concept is essential for solving various geometry problems involving triangles and can help in proving other geometric properties and theorems.