What is the sum of the angles in a triangle?

The sum of the angles in a triangle is always 180 degrees, regardless of the type of triangle. This fundamental property arises from the definition of geometric shapes and can be demonstrated through various methods, such as using parallel lines and alternate interior angles.

When you draw a triangle and extend one of its sides, you can show that the exterior angle formed is equal to the sum of the two opposite interior angles. This reinforces that for any triangle, the three interior angles add up to exactly 180 degrees.

This property is essential in various applications of geometry, including solving problems related to triangle congruence, similarity, and trigonometry, making it a cornerstone concept in understanding triangles and their properties.