1. **Problem statement:** We have three similar triangles with given angles and side lengths. We need to find the values of $w$, $x$, and $y$. 2. **Recall properties of similar triangles:** Corresponding angles are equal, and corresponding sides are proportional. 3. **Find missing angles:** - For the first triangle, angles are $56^\circ$, $94^\circ$, and the third angle is $180^\circ - 56^\circ - 94^\circ = 30^\circ$. - For the second triangle, since it is similar to the first, angles are $w^\circ$, and the other two angles correspond to $56^\circ$ and $94^\circ$ or $30^\circ$. - For the third triangle, angles given are $30^\circ$ and $56^\circ$, so the third angle is $180^\circ - 30^\circ - 56^\circ = 94^\circ$. 4. **(a) Find $w$:** Since the second triangle is similar to the first, and the first triangle's angles are $56^\circ$, $94^\circ$, and $30^\circ$, the second triangle's angles must be the same set. Given the second triangle has an angle $w^\circ$ opposite side 4 cm, and sides 4 cm, 8 cm, and $y$ cm, the angle $w$ corresponds to the $30^\circ$ angle in the first triangle (since 4 cm corresponds to 6 cm in the first triangle, the smallest side opposite the smallest angle). Therefore, $w = 30^\circ$. 5. **(b) Find $x$:** The third triangle has angles $30^\circ$, $56^\circ$, and $94^\circ$, same as the first triangle, so they are similar. Corresponding sides between the first and third triangles: - Side opposite $30^\circ$ in first triangle is 6 cm. - Side opposite $30^\circ$ in third triangle is 20 cm. Scale factor from first to third triangle is $\frac{20}{6} = \frac{10}{3}$. Side $x$ in the third triangle corresponds to side 12 cm in the first triangle (opposite $94^\circ$). So, $$x = 12 \times \frac{10}{3} = 40$$ 6. **(c) Find $y$:** The second triangle has sides 4 cm, 8 cm, and $y$ cm. Corresponding sides between first and second triangles: - Side 6 cm in first triangle corresponds to 4 cm in second triangle. Scale factor from first to second triangle is $\frac{4}{6} = \frac{2}{3}$. Side $y$ in second triangle corresponds to side 12 cm in first triangle. So, $$y = 12 \times \frac{2}{3} = 8$$ **Final answers:** $$w = 30^\circ, \quad x = 40, \quad y = 8$$