Given that, simple graph $G$ has $n = 10$ vertices, $e = 11$ edges.
Let say, the number of edges in the complement of $G$ is $x.$
We know that, $e + x = \;^{n}C_{2}$
$\implies e + x = \dfrac{n(n-1)}{2}$
$\implies 11 + x = \dfrac{10\cdot 9}{2} = 45$
$\implies x = 45 – 11 = 34.$
Hence, he number of edges in the complement of $G$ is $x = 34$ edges.
So, the correct answer is $34.$