1. The problem asks for the measure of angle $\angle B$ in the hexagon with given interior angles: $\angle A = 120^\circ$, $\angle B = 129^\circ$, $\angle C = 148^\circ$, $\angle D = 90^\circ$, $\angle E = 142^\circ$, and $\angle F = 130^\circ$. 2. Since the measure of $\angle B$ is already given as $129^\circ$, the answer is directly $129^\circ$. 3. To confirm, the sum of interior angles of a hexagon is given by the formula: $$\text{Sum of interior angles} = (n-2) \times 180^\circ$$ where $n=6$ for a hexagon. 4. Calculate the sum: $$ (6-2) \times 180^\circ = 4 \times 180^\circ = 720^\circ $$ 5. Sum the given angles: $$120^\circ + 129^\circ + 148^\circ + 90^\circ + 142^\circ + 130^\circ = 759^\circ$$ 6. The sum is $759^\circ$, which is slightly off from $720^\circ$, indicating a possible error in the problem statement or measurements, but since $\angle B$ is given as $129^\circ$, that is the measure. **Final answer:** $$m\angle B = 129^\circ$$