What is the sum of angles in a triangle?

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

To understand this better, consider the following: when you draw a triangle, the three corners, known as vertices, all contribute to the total angle measurement. For any triangle, if you take one of the angles and extend a line along one of its sides, you can visualize how the angles relate to each other. Drawing this additional line creates an external angle which, when summed with the internal angles, reinforces that they always total 180 degrees.

This characteristic is used in many areas of mathematics, including geometry, trigonometry, and even higher-level applications. It's crucial for solving problems related to polygons, as well as proving various theorems involving triangles. Understanding that the sum of the angles in a triangle is 180 degrees is essential for any geometric analysis.