What is the sum of the angles in a triangle?

The sum of the angles in a triangle is always 180°. This is a fundamental property in Euclidean geometry, which applies to all triangles regardless of their type (scalene, isosceles, or equilateral).

To understand why this is true, you can visualize or draw a triangle and label its angles as A, B, and C. If you were to extend one side of the triangle, you would be able to create a linear pair of angles that sum to 180° with one of the internal angles of the triangle. By applying this concept to all three angles, you can deduce that A + B + C will also equal 180°.

This specific property makes it fundamental in various applications and proofs in geometry, ensuring that calculations involving triangles consistently yield reliable results. Other choices, like 90°, 360°, and 270°, do not reflect the properties of triangle geometry, since they either represent the sum of angles in different geometric figures or do not adhere to triangle angle sum rules.