(C) ![x=12](/tpl/images/0448/4659/555c2.png)
Step-by-step explanation:
Given: It is given that OP is parallel to NQ and ON=7, NM=21. PQ=x, QM=36.
To find: The value of x.
Solution: It is given that OP is parallel to NQ and ON=7, NM=21. PQ=x, QM=36, thus using the proportionality theorem, we get
![\frac{ON}{OM}=\frac{PQ}{PM}](/tpl/images/0448/4659/4daea.png)
Substituting the given values, we have
![\frac{7}{7+21}=\frac{x}{x+36}](/tpl/images/0448/4659/178f8.png)
Upon solving the above equation, we get
![\frac{7}{28}=\frac{x}{x+36}](/tpl/images/0448/4659/b184b.png)
![\frac{1}{4}=\frac{x}{x+36}](/tpl/images/0448/4659/5a6b3.png)
![x+36=4x](/tpl/images/0448/4659/6bdd2.png)
![x=12](/tpl/images/0448/4659/555c2.png)
Hence, the value of x is 12 and option C is correct.