Magic Pentagon  all sides add up to 100
Magic Pentagon  All sides add up to 100
Michael and his family are utterly stumped at the question below. We have looked at similar problems on your site and been able to get as far as the below. Can you indicate to me where to go next?
Here is the problem and where I have gone
Complete the magic pentagon by putting numbers in the empty circles so that the sum of the three numbers along each of the sides of the pentagon equals 100. Show that there is only one solution to this problem.
The pentagon is
 21 
10 31
 
56 47

I found this confusing because instead of the usual one digit numbers in magic pentagon there are two digit numbers as well.
When I add the pentagon’s sides as all the numbers on 1 side add up to 100 and there are 5 sides the numbers must all add up to 500 but that will be the same as adding all ten numbers and then adding the five corner numbers again. This says that 136 (the sum of the known numbers) plus double the sum of the corner numbers must equal to 500, so double the sum of the corner numbers is 364 and the sum of the corner numbers is 182. So, ...............
Thanks for your help
Michael