why did britain and france declare war on hitler after the invasion of poland?

After Hitler had already annexed Austria and annexed most of Czechoslovakia and then said he planned to invade invaded Poland to get Germans more "lebensraum" (i.e., living room), his hegemony became increasingly clear to everyone, especially to the UK, France, and the USSR, particularly given what he'd said in Mein Kampf, so the UK and France drew a line in the sand and said that enough was enough, that they weren't going to sit idly by as he took over Europe gathering more and more strength, and that if he invaded Poland, it would be war. 

Meanwhile, the USSR entered the Treaty of Non-Aggression with Germany, knowing full well it was all buIIshit and that Hitler planned to have Germany invade the USSR, too, because he said as much in Mein Kampf, said Slavs, the race he said Russians belonged to, were subhuman and needed to be wiped off the face of the Earth, and used Soviet communism as his proof that Slavs were subhuman. Stalin signed the Treaty of Non-Aggression on behalf of the USSR and divided up Poland with Nazi Germany for the same reason Hitler proposed it: to buy time. The USSR needed time to prepare for war and Germany needed time to fell its enemies to the west, namely France and the UK, Hitler knowing full well that both would make good on their threats, all before going to war with the USSR because Hitler knew how foolhardy it would be to divide the Germany army and go to war on two fronts. So then it became a race between whether Stalin could ready the USSR for war before Hitler could defeat France and the UK and so be able to turn the full might of the German army on the USSR. Hitler, wanting the advantage of first-strike, made the fatal error of counting his chickens before they were hatched when he assumed the fall of the UK was imminent and attacked the USSR, so when the UK didn't fall, he suddenly had the war he feared he couldn't win, a war that divided the Germany army in half onto two fronts: the Western Front and the Eastern Front.

Of course, he made another fatal error when he enlisted Japan to attack Pearl Harbor in exchange for all the oil in the Dutch West Indies after he'd conquered the Netherlands. He assumed Roosevelt would never be so foolhardy as to enter the United States into a state of total war on two fronts, so by involving the US in a war with Japan assumed FDR would stay out of the European theater. It turned out that Roosevelt, figuring that that's what Hitler expected, took the advantage by doing what Hitler didn't expect and didn't want, which was having the US declare war on Germany and enter the European theater, thus mitigating the risk of going to war on two fronts, a risk that was further mitigated by the fact that the war wasn't actually fought on American shores and he had the advantage of being able to convert America's entire economy, its entire industrial might, into a giant war machine whose operations could go unfettered and wouldn't be interrupted or interfered with by war on American soil. And so FDR pulled off what Hitler couldn't: successfully waging a state of total war on two fronts, even two fronts that couldn't be further apart from each other and thus thoroughly dividing the US's military might in two.

On September 3, 1939, in response to Hitler's invasion of Poland, Britain and France, both allies of the overrun nation declare war on Germany.

As they are allies and they wouldn't be allies if they left them to die. Also, Hitler broke the law that disallowed Germany from holding weapons after WW1. There is obviously more explanation to this but I just put, what I think is the simplest answer. Please correct me if I'm wrong.

Germany Knew that France and the UK and a Defence Pact with poland

Proving Hitler wanted war with the UK and France

Because they had a military defence treaty with Poland.

Hitler was told not to do it.  And he did.  WW2 in a nutshell.

Because the Nazis were evil and trying to conquer Europe and control the world.

Not that complicated really. 

They had an alliance with Poland.