Answer:
(C) [tex]x=12[/tex]
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
[tex]\frac{ON}{OM}=\frac{PQ}{PM}[/tex]
Substituting the given values, we have
[tex]\frac{7}{7+21}=\frac{x}{x+36}[/tex]
Upon solving the above equation, we get
[tex]\frac{7}{28}=\frac{x}{x+36}[/tex]
[tex]\frac{1}{4}=\frac{x}{x+36}[/tex]
[tex]x+36=4x[/tex]
[tex]x=12[/tex]
Hence, the value of x is 12 and option C is correct.
