One of the basic theorems explaining the properties of a triangle is the exterior angle theorem. If the figure is regular all the exterior angles will be equal. The side opposite to the largest angle of a triangle is the largest side. For more on this see Triangle external angle theorem. Properties. This is called the exterior angle property of a triangle. For more on this see Triangle external angle theorem. For a triangle: The exterior angle d equals the angles a plus b.; The exterior angle d is greater than angle a, or angle b. The exterior angle theorem is Proposition 1.16 in Euclid's Elements, which states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles. Any exterior angle of the triangle is equal to the sum of its interior opposite angles. Apply this relationship to find unknown angles. Exterior Angle Theorem. Types of triangles. Before we begin the discussion, let us have look at what is a triangle. In any geometrical figure, whether regular or irregular, and with any number of sides, the sum of the exterior angles will always be 360 degrees. The exterior angle theorem is amongst the most basic theorems of triangles in geometry. If the equivalent angle is taken at each vertex, the exterior angles always add to 360° In fact, this is true for any convex polygon, not just triangles. Triangles can be classified in 2 major ways: Classification according to internal angles Properties. ; If the equivalent angle is taken at each vertex, the exterior angles always add to 360° In fact, this is true for any convex polygon, not just triangles. Prove that it is equal to the sum of the interior angles on the other two arms. Similarly, this property holds true for exterior angles as well. ∴ Exterior angle is equal to sum of interior opposite angles Find exterior angle ∠ 1 Here, ∠1 = ∠B + ∠C ( Exterior angle property) ∠1 = 45° + 60° ∠1 = 105° Find exterior angle In ∆ABC, ∠BCD = ∠CAB + ∠ABC (Exterior angle property) ∠BCD = 85° + 25° ∠BCD = 110° Find exterior angle In ∆PQR, This is a fundamental result in absolute geometry because its proof does not depend upon the parallel postulate.. An exterior angle of a triangle is equal to the sum of the opposite interior angles. Exterior Angle Property. Also, each interior angle of a triangle is more than zero degrees but less than 180 degrees. In this article, we will learn about: Triangle exterior angle theorem, exterior angles of a triangle, and, how to find the unknown exterior angle of a triangle. Same goes for exterior angles. Property 3: Exterior Angle Theorem An exterior angle of a triangle is equal to the sum of the two opposite interior angles. 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