1. **State the problem:** We are given a hexagon with interior angles measuring 150°, 80°, 120°, 165°, 130°, and an unknown angle $v$. We need to find the value of $v$. 2. **Formula for sum of interior angles of a polygon:** The sum of interior angles of an $n$-sided polygon is given by: $$\text{Sum} = (n-2) \times 180^\circ$$ For a hexagon, $n=6$, so: $$\text{Sum} = (6-2) \times 180^\circ = 4 \times 180^\circ = 720^\circ$$ 3. **Set up the equation:** The sum of all interior angles is 720°, so: $$150^\circ + 80^\circ + 120^\circ + 165^\circ + 130^\circ + v = 720^\circ$$ 4. **Add the known angles:** $$150 + 80 + 120 + 165 + 130 = 645$$ 5. **Solve for $v$:** $$645 + v = 720$$ $$v = 720 - 645$$ $$v = 75$$ 6. **Answer:** The unknown angle $v$ measures $75^\circ$.