1. **State the problem:** We have two similar polygons and need to find the scale factor and the values of $x$, $y$, and $z$. 2. **Given:** Scale factor = 1.67, $x=25$, $y=20$, $z=18$ (to verify). 3. **Formula for scale factor:** $$\text{Scale factor} = \frac{\text{corresponding side length in larger polygon}}{\text{corresponding side length in smaller polygon}}$$ 4. **Check scale factor with given sides:** - Smaller polygon sides: 15 (left), 12 (bottom), 9 (right), $z$ (top) - Larger polygon sides: $x$ (left), $y$ (bottom), 15 (right), 30 (top) 5. **Calculate scale factor from left sides:** $$\frac{x}{15} = 1.67 \implies x = 15 \times 1.67 = 25.05 \approx 25$$ 6. **Calculate scale factor from bottom sides:** $$\frac{y}{12} = 1.67 \implies y = 12 \times 1.67 = 20.04 \approx 20$$ 7. **Calculate scale factor from right sides:** $$\frac{15}{9} = \frac{15}{9} = 1.67$$ (matches scale factor) 8. **Calculate scale factor from top sides:** $$\frac{30}{z} = 1.67 \implies z = \frac{30}{1.67} = 17.96 \approx 18$$ 9. **Summary:** The given values $x=25$, $y=20$, and $z=18$ are consistent with the scale factor 1.67. **Final answers:** - Scale factor = 1.67 - $x = 25$ - $y = 20$ - $z = 18$