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You are watching: The measure of an exterior angle of a triangle is equal to the sum of the measures of the two

Exterior angles in a Triangle snucongo.org Topical summary | Geometry synopsis | MathBits" Teacher sources Terms that Use contact Person: Donna Roberts

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An exterior edge of a triangle is an angle created by one next of the triangle and also the expansion of an adjacent side the the triangle.
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FACTS: • Every triangle has 6 exterior angles, two at every vertex.• angles 1 through 6 space exterior angles.• an alert that the "outside" angle that room "vertical" to the angles inside the triangle space NOT referred to as 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 steps of the two non-adjacent internal angles. (Non-adjacent interior angles may also be described as remote interior angles.)
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FACTS: • one exterior ∠ is same to the addition of the two Δ angles not right next to it. 140º = 60º + 80º; 120º = 80º + 40º; 100º = 60º + 40º • an exterior angle is supplementary come its surrounding Δ angle. 140º is supp to 40º • The 2 exterior angles at each vertex space = in measure because they room vertical angles. • The exterior angle (taken one at a vertex) always total 360º
Solution: utilizing the Exterior angle Theorem 145 = 80 + x x = 65 Now, if you forget the Exterior angle Theorem, you can still gain the price by noticing that a directly angle has actually been created at the vertex of the 145º angle. See example 2.
Solution: i forgot the Exterior edge Theorem. The angle adjacent to 145º will form a directly angle along with 145º adding to 180º. The angle is 35º. Now use preeminence that amount 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