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Lesson 11 2 Angle Theorems for Triangles Answer Key Form

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all right one way we can find missing angle measures and triangles is to use the exterior angle theorem and the exterior angle theorem tells you that the measure of an exterior angle is equal to the sum of its remote interior angles and the remote interior angles are the interior angles of the triangle that are not next to the exterior angle so we have two remote interior angles and the sum of these must be equal to the exterior angle so we can then say that 9 x plus 4 plus 4 x plus 1 has to equal 83 degrees now we can solve for x by combining like terms 9 x's and 4 x's is 13x positive 4 and a positive 1 gives me a positive 5. so we've got 13x plus 5 equals 83. now this is a two-step equation we want to get the x by itself so we're going to first subtract 5 from both sides give us 13 x equals 83 minus 5 78 and then we divide both sides by 13 and we get x equals 6. so now we know that x is 6 we can plug 6 in to either of these 9 times 6 is 54 plus 4 so an

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