Find two consecutive whole numbers that 90 lies between

Let
a> the first whole number
a+1> the second consecutive whole number

we know that
if   90 lies between
then 
[a+(a+1)]/2=90> 2a+1=180> a=179/2> a=89.5
a=89.5
a+1=90.5
but 
89.5 and 90.5 are not whole numbers

therefore
No solutions exist

the answer is
No solutions exist