How did the british defeat of the spanish armada pave the way for bristish colonies

Probably the most basic answer is that with the mighty Spanish Armada out of commission, it opened the door for the exploration of the American continent by the French and the British. As these two nations built up colonies in the "new world" they became more and more wealthy. Britain, which hadn't nearly enough farmland to outfit an army, and a shortage of lumber that made naval expansion difficult, sought both of these things in the American continent. As they harvested lumber, they built bigger and better ships, which could haul more grain and outfit more firepower, which in turn helped them to secure even more of the continent. 

This sentence is true.