The value of x is 12.7 units and the correct option is C.
Since LP is parallel to MO, we have the following alternate interior angles:
<LPM = <MNO
<LPN = <MON
We are also given that the length of PN is 11.25 units.
From <LPM = <MNO, we have the following proportion:
LP / MO = LM / MN
Substituting in the given values, we get:
x / 9 = 8 / 11.25
Cross-multiplying and solving for x, we get:
x = 9 * 8 / 11.25
= 12.7
Therefore, the value of x is 12.7 units.