Answer
$-1.28\sigma$, $1.28\sigma$
Work Step by Step
The B/C cutoff has an area of 0.10 to the left. Use a z-table (inverse mode), we can find $z\approx-1.28\sigma$
The A/B cutoff has an area of 0.90 to the left. Use a z-table (inverse mode), we can find $z\approx1.28\sigma$