1. **State the problem:** We have a pentagon with five internal angles labeled as $135^\circ$, $62^\circ$, $(n+6)^\circ$, $n^\circ$, $140^\circ$, and $151^\circ$. We need to find the value of $n$. 2. **Recall the formula for the sum of interior angles of a polygon:** For a polygon with $k$ sides, the sum of interior angles is given by: $$\text{Sum} = (k-2) \times 180^\circ$$ Since this is a pentagon, $k=5$, so: $$\text{Sum} = (5-2) \times 180^\circ = 3 \times 180^\circ = 540^\circ$$ 3. **Set up the equation:** The sum of all interior angles must equal $540^\circ$: $$135 + 62 + (n+6) + n + 140 + 151 = 540$$ 4. **Combine like terms:** $$135 + 62 + 6 + 140 + 151 + n + n = 540$$ $$(135 + 62 + 6 + 140 + 151) + 2n = 540$$ Calculate the sum of constants: $$494 + 2n = 540$$ 5. **Solve for $n$:** $$2n = 540 - 494$$ $$2n = 46$$ $$n = \frac{46}{2}$$ $$n = 23$$ 6. **Final answer:** The value of $n$ is $23^\circ$.