To find the measure of angle \( B \) in triangle \( ABC \), we can use the fact that the sum of the measures of the angles in a triangle is always \( 180^\circ \).
Given:
- \( m\angle A = 63^\circ \)
- \( m\angle C = 99^\circ \)
We can set up the equation:
\[ m\angle A + m\angle B + m\angle C = 180^\circ \]
Substituting in the known values:
\[ 63^\circ + m\angle B + 99^\circ = 180^\circ \]
Now, combine the angles \( A \) and \( C \):
\[ 162^\circ + m\angle B = 180^\circ \]
To isolate \( m\angle B \), subtract \( 162^\circ \) from both sides:
\[ m\angle B = 180^\circ - 162^\circ \] \[ m\angle B = 18^\circ \]
Thus, the measure of angle \( B \) is \( 18^\circ \).