Answer:
x = 2
Step-by-step explanation:
Assuming the figure is a rhombus, the diagonal divides the figure into two isosceles triangles. That means the marked angles are congruent:
7x² -8 = 6x² -2x
x² +2x -8 = 0 . . . . . . . subtract 6x²-2x
(x +4)(x -2) = 0 . . . . . factor
x = -4 or x = 2 . . . . . values of x that make the factors zero
The only value of x that makes sense in this problem is ...
x = 2
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Additional comment
We know the base angles of an isosceles triangle must be less than 90°. As the attached graph shows, the angle measures for x=-4 would both be 104°, an impossible situation for this geometry.
