Apoint mutation changes the dna sequence cga to cgt, but the same protein is still produced. which point mutation occured?

The answer is the silent mutation.

The types of point mutations are nonsense (where the change results in a premature stop codon), missense (where the change results in a codon coding for a different amino acid), silent (where the change will have no effect on the amino acid), and frameshift (where the addition or deletion of a base causes a totally different translation to amino acids).

In nonsense, missense, and frameshift, it results in a different amino acid being coded for. The silent mutation causes a change in the base, which leads to a change in the codon, but still codes for the same amino acid, therefore the same protein is produced. Since the problem states that the same protein is produced, it would be a silent mutation.