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Solve for x

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novjb | Salutatorian

Posted September 12, 2013 at 4:39 PM via web

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Solve for x

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tiburtius | High School Teacher | (Level 3) Associate Educator

Posted September 12, 2013 at 6:15 PM (Answer #1)

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First let's call the vertex between D and C E and the one between A and D (next to x) F.



And since the sum of angles in a triangle is constant (equal to 180°) it follows that the third angles are also equal that is


Now since all three angles are equal it follows that the triangles CDE  and AFD are similar, hence their sides must be proportional so we have


Since ABCE is parallelogram `|AB|=|CD|=>|AB|=7.5`  also `|AB|=|DC|=>|DC|=5`

So we have



`x=6`   <-- Your solution

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