If the given geometric figure is a parallelogram, then the angle `3x = 7y - 2` and `9y = 4x + 1` , since they are alternate interior angles formed by the transversal diagonal and the parallel lines of parallelogram.

You need to solve the following system of equations such...

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If the given geometric figure is a parallelogram, then the angle `3x = 7y - 2` and `9y = 4x + 1` , since they are alternate interior angles formed by the transversal diagonal and the parallel lines of parallelogram.

You need to solve the following system of equations such that:

`{(3x = 7y - 2),(9y = 4x + 1):}` => `{(3x- 7y =- 2),(-4x + 9y = 1):}` => `{(12x- 28y =- 8),(-12x + 27y = 3):}` `=> -y = -5` => y = 5

`3x = 7*5 - 2 => 3x = 35 - 2 => 3x = 33 => x = 11`

**Hence, evaluating x and y, using the property of parallelogram and alternate interior angles, yields `x = 11 ` and `y = 5` .**