What is the sum of the interior angles of a triangle?

The sum of the interior angles of a triangle is 180 degrees. This property arises from the fundamental nature of triangles in Euclidean geometry. When you draw a triangle, each of its angles contributes to the overall shape, and they combine to create a straight line. In fact, if you were to draw a line through one of the vertices of the triangle that extends parallel to the opposite side, you can see how the angles on the interior of the triangle and those formed at the intersection with the parallel line must together equal 180 degrees because they form a linear pair.

Understanding this property is key in solving many geometry problems, as it can also be used to determine the measure of one angle if the measures of the other two angles are known. Overall, this foundational concept is essential in the study of triangles and serves as a basis for more complex geometric concepts.