im taking geometry A and i have a hard time with the keeping the properties straight in mathematical reasoning. the question im struggling with at the moment is in the picture here:thank you for your time

The given proposition is
[tex]m\angle UJN=m\angle EJN\rightarrow m\angle UJN+m\angle YJN=m\angle EJN+m\angle YJN[/tex]As you can observe, it was added angle YJN to the equation on both sides. The property that allows us to do that it's call addition property of equalities.