1. **State the problem:** We have a pentagon with interior angles labeled as $80^\circ + y^\circ$, $62^\circ$, $95^\circ + x^\circ$, $53^\circ$, and $z^\circ$. We need to find the values of $x$, $y$, and $z$. 2. **Formula used:** The sum of interior angles of a polygon with $n$ sides is given by: $$\text{Sum of interior angles} = (n-2) \times 180^\circ$$ For a pentagon, $n=5$, 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 is: $$ (80 + y) + 62 + (95 + x) + 53 + z = 540 $$ 4. **Combine like terms:** $$ 80 + y + 62 + 95 + x + 53 + z = 540 $$ $$ (80 + 62 + 95 + 53) + (x + y + z) = 540 $$ $$ 290 + (x + y + z) = 540 $$ 5. **Isolate the variables:** $$ x + y + z = 540 - 290 $$ $$ x + y + z = 250 $$ 6. **Interpretation:** The sum of $x$, $y$, and $z$ is $250^\circ$. Without additional information or relationships between $x$, $y$, and $z$, we cannot find their individual values. **Final answer:** $$ x + y + z = 250^\circ $$