Final answer:
The question requires understanding the Segment Addition Postulate to find the correct value of x and the lengths of HJ and JK on segment HK, which has a total length of 18. Each of the provided options agrees with the postulate and could be the solution depending on how segment HK is divided.
Step-by-step explanation:
To find the value of x and each segment length, we can use the segment addition postulate. The segment addition postulate states that if three points A, B, and C are collinear, then AB + BC = AC.
a. Given HK = 18 and HJ + JK = HK, we can substitute the values and solve for x: 6 + 12 = 18, so x = 6. Therefore, HJ = 6 and JK = 12.
b. Given HK = 18 and HJ + JK = HK, we can substitute the values and solve for x: 8 + 10 = 18, so x = 8. Therefore, HJ = 8 and JK = 10.
c. Given HK = 18 and HJ + JK = HK, we can substitute the values and solve for x: 9 + 9 = 18, so x = 9. Therefore, HJ = 9 and JK = 9.
d. Given HK = 18 and HJ + JK = HK, we can substitute the values and solve for x: 12 + 6 = 18, so x = 12. Therefore, HJ = 12 and JK = 6.