Is this Quadrilateral a Parallelogram?

The diagram shows the quadrilateral ABCD (not to scale). Is it a parallelogram?

Given that

$A = 3 x^{2} + 5 x$ , $B = x^{2} - x$ , $C = 30 x + 50$ and $D = 11 x - 20$

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In a parallelogram, opposite angles are equal, therefore,

30 x + 50 = 3 x^{2} + 5 x

and

11 x - 20 = x^{2} - x

Simplifying, we get,

3 x^{2} - 25 x - 50 = 0

and

x^{2} - 12 x + 20 = 0

These have solutions,

x = {10, - \frac{5}{3}}

and

x = {10, 2}

So, if $x = 10$ then the quadrilateral is a parallelogram.

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