To solve this problem, we use the Law of Cosines.
Using the Law of Cosines, we get that:
[tex]2\sqrt{13}=\sqrt{2^2+6^2-2(2)(6)cosA}.[/tex]
Solving the above equation for cosA, we get:
[tex]\begin{gathered} 4(13)=4+36-24cosA, \\ 52=40-24cosA, \\ 24cosA=-12, \\ cosA=\frac{-12}{24}=-\frac{1}{2}. \end{gathered}[/tex]
Therefore:
[tex]A=120^{\circ}.[/tex]
Answer:
[tex]\begin{equation*} 120^{\circ}. \end{equation*}[/tex]
