What is the sum of the angles in a triangle?

The sum of the angles in a triangle is always 180 degrees. This is a fundamental property in Euclidean geometry, which states that when you take any triangle, regardless of its type (scalene, isosceles, or equilateral), the three interior angles will add up to exactly 180 degrees.

This property can be understood through various methods, such as drawing parallel lines and using alternate interior angles, or by dividing a triangle in a certain way to illustrate that the angles correspond to linear angles that add up to a straight line (180 degrees).

For example, if a triangle has one angle measuring 60 degrees and another measuring 70 degrees, the third angle can be calculated as 180 - (60 + 70) = 50 degrees. Summing them gives 60 + 70 + 50 = 180 degrees.

This rule is essential for understanding various concepts in both geometry and trigonometry, and is foundational for solving problems involving triangles in different contexts.