Just another counting problem

An integer is called a $20$ -number if the sum of its digits is equal to $20.$ How many even $20$ -numbers are there less than or equal to $\numcomma{100000}$ ?

For example, $758,$ $\numcomma{19730},$ and $\numcomma{44552}$ are $20$ -numbers because

$7+5+8=20, 1+9+3+7+0=20, \text{ and } 4+4+5+5+2=20 .$