The button has fairly aggro stats, so I think he will be raising all of his Ax and Kx combo's here. Since he doesn't bet out on the flop, I'm almost certain he didn't have an fdraw on the flop either. If he had some kind of draw like T9 or 65, I'm pretty sure he would have bet that out as well. So I thought this was a perfect turn to take the pot down, thoughts?
His stats:
58/28/5.0 agg f.
Ongame Network NL Hold'em Turbo No Limit Hold'em Tournament - t50/t100 Blinds - 4 players - View hand 1602147
DeucesCracked Poker Videos Hand History Converter
BTN: t2105 21.05 BBs
SB: t1675 16.75 BBs
Hero (BB): t1300 13 BBs
CO: t2420 24.20 BBs
Pre Flop: (t150) Hero is BB with 4 
Q 
1 fold, BTN calls t100, 1 fold, Hero checks
Flop: (t250) 7 8 7 (2 players)
Hero checks, BTN checks
Turn: (t250) K (2 players)
Hero bets t180, BTN folds