To find the measure of angle \( B \) in triangle \( \triangle ABC \), we can use the fact that the sum of the angles in a triangle is always \( 180^\circ \). This means:
\[ m\angle A + m\angle B + m\angle C = 180^\circ \]
We know that:
- \( m\angle A = 63^\circ \)
- \( m\angle C = 99^\circ \)
Substituting the known values into the equation, we have:
\[ 63^\circ + m\angle B + 99^\circ = 180^\circ \]
Now, combine \( 63^\circ \) and \( 99^\circ \):
\[ 162^\circ + m\angle B = 180^\circ \]
Next, subtract \( 162^\circ \) from both sides to isolate \( m\angle B \):
\[ m\angle B = 180^\circ - 162^\circ = 18^\circ \]
Thus, the measure of angle \( B \) is:
\[ \boxed{18^\circ} \]