1. **Problem Statement:** We have a kite-shaped quadrilateral GHJI with diagonals GI and JH intersecting at point F. We are given that segment JI is 85 units, and segment JF is 36 units. We need to find the length of FI. 2. **Properties of Kites:** In a kite, the diagonals are perpendicular, and one diagonal (usually the one connecting the vertices between the two pairs of equal sides) is bisected by the other. Here, diagonal JH is bisected by GI at F, so F is the midpoint of JH. 3. **Using the Midpoint Property:** Since F is the midpoint of JH, segment JF equals segment FH. Given JF = 36, then FH = 36. 4. **Using the Diagonal Length:** The diagonal JI is given as 85 units. Since F lies on GI, and GI is a diagonal, FI is the remaining part of GI after subtracting JF. 5. **Calculate FI:** $$FI = JI - JF = 85 - 36 = 49$$ 6. **Answer:** The length of FI is 49 units.