9. \( \overline{W Y}=(y+3) \mathrm{cm}, \overline{X Z}=(4 y-6) \mathrm{cm} \), find the value of y , lengths of \( \overline{W Y} \) and \( \overline{X Z} \) 10. If \( \angle W Z Y=(3 x-10)^{\circ}, \angle W X Y=(2 x+5)^{\circ} \), what is the value of x ?

Let's tackle each problem step-by-step. --- ### **Problem 9** **Given:** - \( \overline{WY} = (y + 3) \) cm - \( \overline{XZ} = (4y - 6) \) cm **Assumption:** It's likely that segments \( \overline{WY} \) and \( \overline{XZ} \) are equal in length. This is a common scenario in geometric problems involving congruent sides or diagonals. **Set Up the Equation:** \[ \overline{WY} = \overline{XZ} \\ y + 3 = 4y - 6 \] **Solve for \( y \):** \[ y + 3 = 4y - 6 \\ 3 + 6 = 4y - y \\ 9 = 3y \\ y = 3 \] **Find the Lengths:** - \( \overline{WY} = y + 3 = 3 + 3 = 6 \) cm - \( \overline{XZ} = 4y - 6 = 4 \times 3 - 6 = 12 - 6 = 6 \) cm **Answer for Problem 9:** - **Value of \( y \):** 3 - **Length of \( \overline{WY} \):** 6 cm - **Length of \( \overline{XZ} \):** 6 cm --- ### **Problem 10** **Given:** - \( \angle WZY = (3x - 10)^\circ \) - \( \angle WXY = (2x + 5)^\circ \) **Assumption:** Without additional context, a common relationship between two angles in geometric figures is that they are either **supplementary** (their measures add up to 180°) or **congruent** (they are equal). Based on the forms of the expressions, it's reasonable to assume they are **supplementary**. **Set Up the Equation:** \[ \angle WZY + \angle WXY = 180^\circ \\ (3x - 10) + (2x + 5) = 180 \] **Solve for \( x \):** \[ 3x - 10 + 2x + 5 = 180 \\ 5x - 5 = 180 \\ 5x = 185 \\ x = 37 \] **Answer for Problem 10:** - **Value of \( x \):** 37 --- **Summary of Answers:** 1. **Problem 9:** \( y = 3 \); \( \overline{WY} = 6 \) cm; \( \overline{XZ} = 6 \) cm. 2. **Problem 10:** \( x = 37 \).