1. **State the problem:** We have a convex pentagon with interior angles measuring $2v$, $2v + 43^\circ$, $2v + 12^\circ$, $96^\circ$, and $v + 25^\circ$. We need to find the value of $v$. 2. **Recall the formula:** The sum of interior angles of a pentagon is given by $$ (5 - 2) \times 180^\circ = 3 \times 180^\circ = 540^\circ.$$ 3. **Set up the equation:** Sum of all angles equals $540^\circ$: $$2v + (2v + 43) + (2v + 12) + 96 + (v + 25) = 540.$$ 4. **Combine like terms:** $$2v + 2v + 43 + 2v + 12 + 96 + v + 25 = 540$$ $$ (2v + 2v + 2v + v) + (43 + 12 + 96 + 25) = 540$$ $$7v + 176 = 540.$$ 5. **Solve for $v$:** $$7v = 540 - 176$$ $$7v = 364$$ $$v = \frac{364}{7}$$ $$v = 52.$$ 6. **Answer:** The value of $v$ is $52^\circ$.