Final answer:
The request concerns finding angles in an isosceles triangle but provides details related to physics concepts. Without clear geometrical context or a diagram, it's not possible to accurately determine the values of angles m and n.
Step-by-step explanation:
To find the value of angles m and n in an isosceles triangle with a vertex angle, we would typically use the properties of an isosceles triangle and basic trigonometry. However, the provided information seems to refer to physics-related concepts, such as interference patterns and angles of inclination in scattering problems, rather than a geometrical isosceles triangle. Without a clear connection to these physics concepts or further information on the geometry of the triangle in question, it is not possible to provide a definitive answer to find the values of angle m and angle n.