# Why do the angles in a triangle add up to 180 degrees?

The sum of the interior angles of a triangle is based on the concepts of Euclidian geometry, particularly the triangle postulate which states that the sum of the angles of any triangle is equivalent to two right (or 90-degree) angles.

While there are many postulates, axioms and theorems that support the 180-degree triangular summation, the most popular proof is through the concept of a straight line parallel to one of the sides of the triangle and passing through the vertex opposite the aforementioned side.

To better understand this, think of a triangle ABC with one of its sides horizontal or laying on the ground. Imagine a line parallel to the horizontal side (say, side AB) and passing through the top vertex (in this case, vertex C). The intersection between the line and the triangle through vertex C will form three angles: the interior angle at vertex C and two exterior angles bound by the horizontal line and the two triangle sides through vertex C.

Based on the theorem that alternate interior angles formed by a line intersecting two parallel lines are equal, it can be said that the two exterior angles at vertex C are equal to their corresponding alternate interior angles, which happen to be the interior angles at vertices A and B.

In other words, the sum of the triangle's interior angles is equal to the angle formed by a straight line, which is 180 degrees.

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Q&A Related to "Why do the angles in a triangle add up to 180..."
 The maximum angle is 360Â°.This is the angle all the way http://www.chacha.com/question/why-do-all-the-angl...
 It is a consequence of Euclids's parallel postulate. http://wiki.answers.com/Q/Why_does_a_triangles_ang...
 4/17/96 at 19:16:32 From: Anonymous Subject: Geometry, angles in a triangle Hi! We were wondering why all the angles in a triangle add up to 180 degrees. Several of us are trying http://mathforum.org/library/drmath/view/57727.htm...
 YES - in non-planar geometry e.g. spherical trigonometry. This is one example of a non-Euclidean geometry. (Hyperbolic geometry would be another) A triangle on the outside of a sphere http://uk.answers.yahoo.com/question/index?qid=200...
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