Triangles LNM and SRT are similar, so corresponding angles are congruent. In particular, angles M and T are congruent. The interior angles of any triangle sum to 180º in measure, so
65º + 55º + (2x + 30)º = 180º
Solve for x :
(2x)º + 30º = 60º
(2x)º = 30º
x = 15