Solve for x

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Expert Answers

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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.

`/_CDE=/_ADF` 

`/_CED=/_DFA=90^o`

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

`/_ECD=/_DAF`

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

`|AD|:|DC|=x:|CE|`

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

So we have

`7.5:5=x:4`

`5x=30`

`x=6`   <-- Your solution

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