Which answer best describes the relationship of the roman catholic church and king henry the 8 of england during the renaissance

 He did NOT form the Anglican Church so he could get divorced. I'll bet many answers here say exactly that. Here is the real story, which is a LOT more complicated. 

Henry was a devout Roman Catholic. This was during the Protestant Reformation in Europe, but, he firmly resisted changes - he even had leading Reformers in England put to death. He was awarded the title "Defender of the Faith" from the pope for his anti-Reform work. He remained Catholic in faith all his life. 

In England, the King was the Head of the Church. They shared things like appointing bishops, etc., with the Pope. The Pope would sent the pilum - an official message (wrapped around a stick, called the pilum) naming who he wanted as bishop, and the king would normally agree, and make the appointment. This had been occurring since the British Church came under the Latin one at the Council of Whitby in 663AD. 

Henry had married his older brother's widow. This was against church canons (laws), and required papal dispensation to do. He saw the lack of a male heir as God's punishment for him. As a very devout man, he sought to have the illegal marriage annulled, which is common with Catholics, even to this day. Divorce was impossible - it was illegal. However, there was a problem - the Pope was being held captive by the Queen's relative, so, the Pope stalled. And stalled, and stalled. 

Meanwhile, England had been paying "Peter's Pence," a tax to the church in Rome. It was pointed out to Henry that this was illegal under English law, as it made Henry vassal to the Pope, which wasn't allowed. So, several things happened over a few years: Henry appointed an Archbishop of Canturbury on his own (without the pilum), who granted the annulment. He also stopped paying the tax, which was being given to the armies of England's enemies anyway. Later on, there was another issue. This was the time of indulgences (which led to the Reformation in the first place), so, right people would leave their lands to the Church in their wills, to be granted indulgences. But, Church lands were officially no longer under English control, and could not be taxed, not the people there called into the military in time of war. By Henry's time, 1/3 of England was in Church hands, and the trend showed no signs of slowing down. Henry dissolved the monasteries, and took back the lands for England. 

Naturally, these things miffed the Pope a bit! Henry was excommunicated. This was a common tactic then, as the Pope was as much a political leader as a religious one, and European kings would be excommunicated until they had "smartened up." However, this meant that the church in England was now officially cut off from Rome, as Henry was the head of it. This was confirmed in law when the English Parliament proclaimed Henry the head officially (even though he always had been). So, the Church in England was separated from the Bishop of Rome - but, nothing else changed of any significance. It was still Catholic, just no longer Roman Catholic. This angered the Reformers. However, being cut off from Rome angered the hard core Catholics. The Church in England became the Church of England, kind of in between the two sides. However, much of that happened in Elizabeth's time. 

Queen Mary was very Roman Catholic, and undid the few changes that Henry eventually allowed (priests could marry, and lessons could be read in English). She was called "Bloody Mary" for all the killings, and executions. So, when Elizabeth took over, she made the Church the "via media," or "middle way" between Roman Catholics, and Reformers. So, the Church of England became Catholic, but not Roman Catholic, and, not quite Protestant either. 

Much of this was pretty much by accident. It was much later that the Anglican Church became more Protestant, under the influence of Puritans, etc. Then, it swung back to Catholic. This has happened quite a few times - currently, the Anglican Church worldwide is pretty close to the Catholics again. Close enough that I as an Anglican attended a Roman Catholic Seminary, as my Anglican diocese had no school of it's own.