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Alternate angles BDF and DFG are equal, so lines BD and FG are parallel.

Therefore angle BCA = angle FGC = $80^{\circ}$ (corresponding angles).

Consider triangle ABC: $x + 70 + 80 = 180$ so $x=30$.

*This problem is taken from the UKMT Mathematical Challenges.**View the archive of all weekly problems grouped by curriculum topic*

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