In a triangle, the sum of the measures of the angles is always 180 degrees.
Given that angle A is 63 degrees and angle C is 99 degrees, we can find the measure of angle B by subtracting the sum of angles A and C from 180 degrees.
Angle B = 180 degrees - (angle A + angle C)
Angle B = 180 degrees - (63 degrees + 99 degrees)
Angle B = 180 degrees - 162 degrees
Angle B = 18 degrees
Therefore, the measure of angle B is 18 degrees.