Should I have accepted the draw?

I am very new to chess and am still learning the etiquite of when to accept a draw. I was in a game where the oponnent had only his king and I had more time. The board looked like the board below. He offered a draw. Should I have accepted his draw or should I have played till he resigned. Once I refused the draw he rage quit and let me sit out the last minute.

No, of course not.

No. He was trying to get out of a loss.

sore loser

How would I have finished this game without just playing time?

It's black's move, he's in check.

If black is stupid enough to play Kf4, then you almost can't help mating. Putting either queen on e5 would do it, among other things.

If black plays Kd3, I don't see a mate in one, and you don't really need to spend time looking for one. Just use your queens to push him to the edge and you can mate easily. Watch out for stalemate.

NO! Why would you accept a draw when you're completely winning?