![]() The polygon exterior angle sum theorem states that "the sum of all exterior angles of a convex polygon is equal to 360°'. Statement: The angle sum theorem states that the sum of all the interior angles of a triangle is 180 degrees. Therefore, ∠R = 8° Angle Sum Theorem Statement ![]() As per the triangle angle sum theorem, ∠P + ∠Q + ∠R = 180° Consider a triangle PQR such that, ∠P = 38° and ∠Q = 134°. Let's consider an example to understand this theorem. Thus, in the given triangle ABC, ∠A + ∠B + ∠C = 180°. As per the triangle sum theorem, the sum of all the angles (interior) of a triangle is 180 degrees, and the measure of the exterior angle of a triangle equals the sum of its two opposite interior angles.įrom the above-given figure, we can notice that all three angles of the triangle when rearranged, constitute one straight angle. 1.Ī triangle is a two-dimensional closed figure formed by three line segments and consists of the interior as well as exterior angles. In this article, we will discuss the angle sum theorem and the exterior angle theorem of a triangle with its statement, proof, and examples. In geometry, the triangle sum theorem has varied applications as it gives important results while solving problems involving triangles and other polygons. A triangle is the smallest polygon having three sides and three interior angles, one at each vertex, bounded by a pair of adjacent sides. In a Euclidean space, the sum of the measure of the interior angles of a triangle sum up to 180 degrees, be it an acute, obtuse, or a right triangle which is the direct result of the triangle sum theorem, also known as the angle sum theorem of the triangle. The triangle sum theorem states that the sum of all the interior angles of a triangle is 180 degrees.
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