4 arithmetic means between two numbers are just four numbers that occur as a sequence between the two numbers, such that they are equidistant from each other. For example, two arithmetic means between 4 and 10 are 6 and 8, because 4, 6, 8, 10 forms an arithmetic sequence with a distance of 2.
For this problem, we need to find four means between 45 and 80. To do this, we can set up an arithmetic sequence and figure out what our distance value (d) has to be. We know that there are six numbers total, and 5 excluding the first one. That means that our common distance is (80-45)/5, or 35/5, which is equal to 7
Our first number after 45 is 45 + 7, or 52
Our second number is 52 + 7, or 59
Our third number is 59 + 7, or 66
Our fourth number is 66 + 7, 73
This checks out because 73 + 7 is 80, which is the max number in our range.
Therefore, the arithmetic means are 52, 59, 66, and