1. **State the problem:** We are given a pentagon with interior angles labeled as $4x$, $(5x + 3)$, $(2x + 1)$, $(4x + 14)$, and $4x$ degrees. We need to solve for $x$. 2. **Recall the formula for the sum of interior angles of a polygon:** For a polygon with $n$ sides, the sum of interior angles is given by: $$\text{Sum of interior angles} = (n - 2) \times 180^\circ$$ Since this is a pentagon, $n = 5$, so: $$\text{Sum} = (5 - 2) \times 180 = 3 \times 180 = 540^\circ$$ 3. **Set up the equation:** The sum of the given angles must equal $540^\circ$: $$4x + (5x + 3) + (2x + 1) + (4x + 14) + 4x = 540$$ 4. **Combine like terms:** $$4x + 5x + 3 + 2x + 1 + 4x + 14 + 4x = 540$$ $$ (4x + 5x + 2x + 4x + 4x) + (3 + 1 + 14) = 540$$ $$19x + 18 = 540$$ 5. **Isolate $x$:** $$19x + 18 = 540$$ $$19x = 540 - 18$$ $$19x = 522$$ 6. **Divide both sides by 19:** $$x = \frac{522}{19}$$ Show cancellation: $$x = \frac{\cancel{19} \times 27.4737}{\cancel{19}}$$ 7. **Calculate the value:** $$x = 27.4737$$ **Final answer:** $$x \approx 27.47$$