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

The sum of the interior angles of a triangle is always 180 degrees, regardless of the type of triangle—whether it's scalene, isosceles, or equilateral. This fundamental property is a result of Euclidean geometry, which dictates that if you take any triangle, the angles measured at each vertex will always add up to 180 degrees.

One way to visualize this is by drawing a triangle and then extending one of its sides. The angles formed outside the triangle alongside the extended line can help illustrate the relationship that leads back to 180 degrees. By rearranging these exterior angles or using methods like angle subtraction, one can see that the original triangle's angles are indeed summing to 180 degrees.

This property is critical in solving various geometry problems and is foundational for understanding more complex shapes and figures. Other choices represent angle sums of different polygons; for example, a quadrilateral has a sum of 360 degrees, and the choices of 90 degrees and 270 degrees do not correspond to any standard polygon interior angle sums. Recognizing that a triangle specifically has a fixed angle sum of 180 degrees is essential in geometry.