Solve this problem: delete due to someone spy
I am quite familiar with Newton’s laws and those introductory mechanics problems and exercises, but I am not going to check whether your reasoning is physically correct.
Either way, this is the correct syntax:
Solve[m*g*Sin[\[Beta]] == \[Mu]s1*m*g*Cos[\[Beta]], \[Beta] ]
I removed the Degree Symbol, and a few [ and ].
Note that you can’t solve for a multipication of two variables in Solve, i.e., you are going to get the message
Solve::ivar: [Degree] [Beta] is not a valid variable.
So if you ask me, solve for the angle beta using Solve and get its value in radians, and convert it to degrees:
Mod[ \[Beta]/Degree,360]
And note that \[Beta] should be inserted as a numerical value.
Good luck!