For more on this see Triangle external angle theorem. Same goes for exterior angles. 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. Define an exterior angle of a triangle and identify all the exterior angles. ; 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. Property 3: Exterior Angle Theorem An exterior angle of a triangle is equal to the sum of the two opposite interior angles. Exterior Angle Property - Displaying top 8 worksheets found for this concept.. Also, each interior angle of a triangle is more than zero degrees but less than 180 degrees. Properties. The exterior angle theorem is amongst the most basic theorems of triangles in geometry. This is called the exterior angle property of a triangle. 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. This is a fundamental result in absolute geometry because its proof does not depend upon the parallel postulate.. 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. A polygon is called a plane figure that is bounded by the finite number of line segments for forming a closed figure. Before we begin the discussion, let us have look at what is a triangle. The side opposite to the largest angle of a triangle is the largest side. Properties. An exterior angle of a triangle is equal to the sum of the opposite interior angles. Exterior Angle Theorem. Property 2: The sum of an interior angle and its adjacent exterior angle is 180°. Prove that it is equal to the sum of the interior angles on the other two arms. Exterior Angle Property. 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. Types of triangles. Triangles can be classified in 2 major ways: Classification according to internal angles Similarly, this property holds true for exterior angles as well. Apply this relationship to find unknown angles. If the figure is regular all the exterior angles will be equal. ∴ 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, 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. Exterior Angle Theorem. For more on this see Triangle external angle theorem. Example: . 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