What is the sum of the angles in a triangle?

• A. 90 degrees
• B. 180 degrees
• C. 270 degrees
• D. 360 degrees

Answer: (B)

The sum of the angles in a triangle is 180 degrees. This property is foundational in geometry and applies to all triangles, regardless of their type (whether they are scalene, isosceles, or equilateral). The reason behind this can be explained through various methods, including geometric proofs.

One common proof involves drawing a line parallel to one side of the triangle. When this line is drawn, it creates alternate interior angles with the angles of the triangle, and by the properties of parallel lines, the sum of these angles equals 180 degrees.

Understanding that all triangles have this angle sum property helps students apply it to various problems in geometry, such as finding missing angles when given the other two angles in a triangle, or in more complex polygons by decomposing them into triangles.