How to sum values across multiple variables using a wildcard?

I have a dataframe called "data" with 5 records (in rows) each of
which has been scored on each of many variables (in columns).

Five of the variables are named var1, var2, var3, var4, var5 using
headers. The other variables are named using other conventions.

I can create a new variable called var6 with the value 15 for each
record with this code:

var6=var1+var2+var3+var4+var5

but this is tedious for my real dataset with dozens of variables. I
would rather use a wildcard to add up all the variables that begin
with "Var" like this pseudocode:

Var6=sum(var*)

Any suggestions for implementing this in R? Thanks! Mark