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

The sum of all angles in a triangle is always 180 degrees. This is a fundamental property of triangles in Euclidean geometry, which applies to all types of triangles, whether they are scalene, isosceles, or equilateral. The reason this sum is always 180 degrees can be understood through the concept of a straight line; when one angle is considered, the other two angles must together create a straight line with it, ultimately leading to a total of 180 degrees when all three angles are combined.

In practical terms, if you were to draw a triangle and extend one of its sides, the angles formed on opposite sides of that line would demonstrate this relationship explicitly. This property is crucial for solving various geometric problems, including determining missing angles and understanding triangle similarity and congruence. As a result, knowing that the sum of the angles in any triangle consistently equals 180 degrees is fundamental to grasping more complex geometric concepts.