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  3. 2 your turn 1 remote interior angles for the figur

2 Your Turn 1 Remote interior angles For the figure shown find the unknown angle...

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Geometry

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2 Your Turn 1 Remote interior angles For the figure shown find the unknown angle measure x For the figure shown find the unknown angle measure x Exterior angle OLUTASH EXPLAIN 3 Using Exterior Angles Read Explain 3 and complete Your Turn 1 2 adapted from Lesson 7 1 Show all your work 0 In the figure to the right we have the interior angles 21 22 and 23 of a triangle We also have the exterior angle 24 of the triangle 140 150 21 22 23 23 24 130 When we extend the side of a polygon the angle formed by the side of the polygon and the extended side is called an exterior angle Exterior angles form linear pairs with the interior angles The remote interior angles of a triangle are the angles that are not adjacent to the exterior angle m21 m2 m 4 Because they form a linear pair 23 and 24 are supplementary So 23 24 180 Also the sum of the measures of any triangle is 180 So 21 22 23 180 After substituting for 180 and simplifying we have 21 22 24 105 Thus the measure of the triangle s exterior angle 24 is equal to the sum remote interior angles 21 and 22 This conjecture can be formally stated as a theorem Exterior Angle Theorem

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