1. **State the problem:** We are given five angles of a hexagon and need to find the measure of the sixth angle. 2. **Recall the formula:** The sum of the interior angles of a polygon with $n$ sides is given by $$\text{Sum of interior angles} = (n - 2) \times 180^\circ.$$ For a hexagon, $n=6$, so $$\text{Sum} = (6 - 2) \times 180 = 4 \times 180 = 720^\circ.$$ 3. **Add the given angles:** The five given angles are $119^\circ$, $129^\circ$, $104^\circ$, $139^\circ$, and $95^\circ$. Their sum is $$119 + 129 + 104 + 139 + 95 = 586^\circ.$$ 4. **Find the sixth angle:** Since the total sum is $720^\circ$, the sixth angle is $$\text{Sixth angle} = 720 - 586 = 134^\circ.$$ 5. **Answer:** The measure of the sixth angle is $134^\circ$.