Given the information on the problem,we have the following triangle:
we can find the measure of angle M using the law of cosine:
[tex]m^2=k^2+l^2-2kl\cos M[/tex]in this case, we have the following:
[tex]\begin{gathered} (69)^2=(76)^2+(30)^2-2(76)(30)\cos M \\ \Rightarrow4761=5776+900-4560\cos M \\ \Rightarrow4761-5776-900=-4560\cos M \\ \Rightarrow-1915=-4560\cos M \\ \Rightarrow\cos M=\frac{-1915}{-4560}=\frac{383}{912} \\ \Rightarrow M=\cos ^{-1}(\frac{383}{912})=65 \\ M=65\degree \end{gathered}[/tex]therefore, the measure of angle M is 65 degrees
