What is the sum of all angles in a triangle?

In any triangle, regardless of its type—be it scalene, isosceles, or equilateral—the sum of the interior angles is always 180 degrees. This fundamental property of triangles is rooted in Euclidean geometry, where the angles within a triangle consistently add up to this specific total.

To understand why this is the case, we can consider a simple proof. If you draw a triangle and extend one of its sides, the angles formed by the extension and the other two sides can be analyzed. You will find that the angle created by the extension and one of the triangle's angles is a straight line, forming a 180-degree angle. Thus, when you add the three interior angles of the triangle, they complement each other to make this total.

This consistent result of 180 degrees has practical implications in various fields, from architecture to engineering, ensuring that designs maintain structural integrity. The other values, such as 90 degrees, 270 degrees, or 360 degrees, do not appropriately represent the sum of interior angles in a triangle, which confirms that 180 degrees is the accurate total.