MTTC 103 Elementary Practice

What is the sum of the angles in a triangle?

1. 180 degrees

2. 360 degrees

3. 90 degrees

4. 270 degrees

The correct answer is: 180 degrees

The sum of the angles in a triangle is always 180 degrees. This fundamental property of triangles is a key aspect of Euclidean geometry. Regardless of the type of triangle—whether it is scalene, isosceles, or equilateral—the internal angles will always add up to 180 degrees. This can be demonstrated through various methods, such as drawing a line parallel to one side of the triangle and using alternate interior angles, or by considering the properties of polygons more generally, where the sum of the internal angles of a polygon is determined by the formula (n-2) × 180 degrees, with n being the number of sides. For a triangle, n equals 3, resulting in (3-2) × 180 = 180 degrees. The other options reflect common misconceptions or the properties of other shapes, rather than the specific characteristics of triangles. For example, a quadrilateral has a sum of angles equal to 360 degrees, while a right-angled triangle has an angle of 90 degrees, but not a sum of 90 degrees for all angles. The sum of the angles in a triangle being 270 degrees is not supported by geometric principles. Thus, the established fact that the sum of the angles in a