# exterior angle property

Exterior Angle Property - Displaying top 8 worksheets found for this concept.. An exterior angle of a triangle is equal to the sum of the opposite interior angles. This is a fundamental result in absolute geometry because its proof does not depend upon the parallel postulate.. If the figure is regular all the exterior angles will be equal. 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. Triangles can be classified in 2 major ways: Classification according to internal angles One of the basic theorems explaining the properties of a triangle is the exterior angle theorem. Define an exterior angle of a triangle and identify all the exterior angles. Property 2: The sum of an interior angle and its adjacent exterior angle is 180°. ∴ 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, For more on this see Triangle external angle theorem. ; 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. Properties. 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. Same goes for exterior angles. Exterior Angle Theorem. The side opposite to the largest angle of a triangle is the largest side. Prove that it is equal to the sum of the interior angles on the other two arms. 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. Property 3: Exterior Angle Theorem An exterior angle of a triangle is equal to the sum of the two opposite interior angles. Types of triangles. 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. A polygon is called a plane figure that is bounded by the finite number of line segments for forming a closed figure. The exterior angle theorem is amongst the most basic theorems of triangles in geometry. Any exterior angle of the triangle is equal to the sum of its interior opposite angles. Let us discuss this theorem in detail. Exterior Angle Theorem. Similarly, this property holds true for exterior angles as well. Exterior Angle Property. 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. Before we begin the discussion, let us have look at what is a triangle. Learn the concepts of Class 7 Maths The Triangle and Its Properties with Videos and Stories. Properties. An exterior angle of a triangle is equal to the sum of the opposite interior angles. Example: . This is called the exterior angle property of a triangle. Apply this relationship to find unknown angles. Also, each interior angle of a triangle is more than zero degrees but less than 180 degrees. For more on this see Triangle external angle theorem. But less than 180 degrees property - Displaying top 8 worksheets found this. An exterior angle of a triangle is equal to the sum of interior... The opposite interior angles on this see triangle external angle theorem the finite number of line for. 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