Answer:
Given that RS bisects MO at N, we know that:
RN = RO (by definition of a bisector)
MN + NO = MO (by the angle bisector theorem)
Given that MN = 5x + 8 and NO = 10 + 3x, we can substitute these values into the second equation to find the value of x.
MN + NO = MO
(5x + 8) + (10 + 3x) = MO
8x + 18 = MO
Now we can use the first equation to find the value of x.
RN = RO
5x + 8 = 10 + 3x
3x = 2
x = 2/3
Therefore, the value of x is 2/3.