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You are watching: Remote interior angles of a triangle definition

Exterior angle in a Triangle aramuseum.org Topical summary | Geometry outline | MathBits" Teacher resources Terms that Use call Person: Donna Roberts

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An exterior edge of a triangle is one angle developed by one side of the triangle and the expansion of an adjacent side of the triangle.
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FACTS: • Every triangle has actually 6 exterior angles, two at each vertex.• angle 1 with 6 space exterior angles.• notification that the "outside" angle that are "vertical" come the angle inside the triangle are NOT dubbed exterior angle of a triangle.
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The measure of an exterior edge of a triangle is same to the sum of the procedures of the 2 non-adjacent interior angles. (Non-adjacent interior angles may also be referred to as remote internal angles.)
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FACTS: • an exterior ∠ is same to the enhancement of the two Δ angles no right beside it. 140º = 60º + 80º; 120º = 80º + 40º; 100º = 60º + 40º • an exterior angle is supplementary to its adjacent Δ angle. 140º is supp come 40º • The 2 exterior angles at each vertex space = in measure because they are vertical angles. • The exterior angle (taken one in ~ a vertex) constantly total 360º
Solution: making use of the Exterior edge Theorem 145 = 80 + x x = 65 Now, if girlfriend forget the Exterior angle Theorem, you deserve to still gain the price by noticing that a directly angle has been developed at the vertex of the 145º angle. See example 2.
Solution: ns forgot the Exterior edge Theorem. The angle adjacent to 145º will form a straight angle along with 145º including to 180º. That angle is 35º. Now use dominion that sum of ∠s in Δ = 180º. 35 + 80 + x = 180 115 + x = 180 x = 65


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Find m∠DBC. Solution:∠BDC is one exterior angle for ΔABD. m∠BDC = 35 + 25 m∠BDC = 60º 180 = m∠DBC + 60 + 60 m∠DBC = 60º