Final answer:
The possible values for m_1 cannot be determined without additional context or information regarding the equations and variables involved.
Step-by-step explanation:
The student is asking for the possible values for m_1 given various pieces of mathematical information. This involves understanding concepts such as angle measurements and perhaps their relationship to trigonometric ratios or physics-related momentum equations, depending on the broader context of the question. However, the question seems to miss the necessary details needed to determine m_1 accurately. It might be a question about solving for a variable in the context of angle measurements or physics-related equations involving momentum and velocity. For example, using a provided equation like m1 sin θ1 - V'1 m2 sin θ2, one could solve for m_1 if the other variables are known. Without clearer context or additional information, it is impossible to give a definitive answer.