There are ten options, but I cannot send all ten at once. Please draw out the correct graph!

To answer this question we need to remember that:
[tex]\sec \theta=\frac{1}{\cos \theta}[/tex]then:
[tex]\begin{gathered} \sec \theta=-\frac{13}{5} \\ \frac{1}{\cos \theta}=-\frac{13}{5} \\ \cos \theta=-\frac{5}{13} \\ \theta=\cos ^{-1}(-\frac{5}{13}) \\ \theta=112.62 \end{gathered}[/tex]There's only one angle that gives this result that it is real. Therefore the answer is 112.62