Anything that causes large amounts of debris and dust to be thrown into the atmosphere will also block some of the suns rays. So, it is a completely plausible (possible) theory that meteors which have struck the Earth in the past have caused this to happen. The typical effect is that the amount of light energy from the sun is diminished, the debris acting sort of like a filter, and the average surface temperature of the Earth can be lowered if enough material is thrown into the upper atmosphere.
As a modern day comparison, I live not far from Mt. St. Helens, in Washington State, and when it erupted in 1980, millions of cubic yards of ash and dust were thrown upwards of 50,000 feet in the air. For almost five year afterwards, the sunsets were a more brilliant red as the debris stayed in the atmosphere that long. That one event did not significantly change the Earth's temperature, but a large enough meteor might.
Some theories suggest ice ages have been caused by large enough impacts, along with the extinction of most species on Earth.
When you say "blocked the sun's rays" do you mean that they were completely blocked so that the Earth was in darkness all the time? If so, then this statement is false.
I assume that you are talking about the impact or impacts of asteroids that caused the break between the Cretaceous and the Tertiary. Scientists believe that there may well have been more than one impact at that time.
Whether there was one impact or more than one, the effect was still the same. A huge amount of dust and debris were ejected into the atmosphere and even out into space. This debris did block the sun's rays, but not for years. Instead, the rays were blocked for a time more on the order of months.
However, I suggest you look in your book because different scientists may differ on how much the sun's rays were blocked and for how long. Your book likely gives the answer you are supposed to come up with.