1. **Problem Statement:** Given parallelogram KLMJ with diagonals intersecting, the segments of the diagonals are given as: - Segment J to intersection: $3y - 5$ - Segment K to intersection: $2z + 7$ - Segment L to intersection: $y + 5$ - Segment M to intersection: $z + 9$ We need to find the values of $y$ and $z$, then find the sum of these values. 2. **Key Property:** In a parallelogram, the diagonals bisect each other. This means the two segments of each diagonal are equal: $$3y - 5 = 2z + 7$$ $$y + 5 = z + 9$$ 3. **Solve the system:** From the second equation: $$y + 5 = z + 9 \implies y - z = 4$$ From the first equation: $$3y - 5 = 2z + 7 \implies 3y - 2z = 12$$ 4. **Substitute $y = z + 4$ into the first equation:** $$3(z + 4) - 2z = 12$$ $$3z + 12 - 2z = 12$$ $$z + 12 = 12$$ $$z = 0$$ 5. **Find $y$ using $y = z + 4$:** $$y = 0 + 4 = 4$$ 6. **Sum of $y$ and $z$:** $$y + z = 4 + 0 = 4$$ **Final answer:** $y = 4$, $z = 0$, and their sum is $4$.