The two items that provide evidence supporting the Big Bang theory are:
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Composition of matter in the universe - This supports the Big Bang theory through the observed ratios of elements, particularly hydrogen and helium, which align with predictions from the theory of Big Bang nucleosynthesis.
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Cosmic background radiation - This is perhaps the most significant evidence for the Big Bang theory, as it is the remnants of the heat from the initial explosion, detected as a uniform background radiation throughout the universe.
So, the correct answers are composition of matter in the universe and cosmic background radiation.