The angles in a linear pair are consecutive odd numbers. What are its measures?

The correct option is A 89 and 91

$x+y={180}^{\circ }$
Consider two consecutive numbers to be 2x + 1 and 2x + 3
$2x+1+2x+3={180}^{\circ }$
$4x+4={180}^{\circ }$
$4x=180-44x=176$
x=44
Then
$2x+1=2\times 44+1=88+1=89$
$2x+3=2\times 44+3=88+3=91$
89 and 91 are 2 two consecutive odd number which forms a linear pair.