If angle x is an acute angle and cos x = t, how do you express cos (180 - x) in terms of t?

Remember that $\cos \left(A - B\right) = \cos A \cdot \cos B + \sin A \cdot \sin B$ hence
cos(180-x)=cos180*cosx+sinx*sin180=(-1)*cosx+sinx*0= -cosx=-t
Finally $\cos \left(180 - x\right) = - t$