Question

so, (3.75)(4) + (.5)(3.75)(49) or 106.875 radians

that's not the correct answer, so is it just the second part to find the additional angle?

(.5)(3.75)(49) = 91.875 but it too is incorrect, what am I missing?

Answer 1

yes that is wrong.
for displacment, the additional displacement,
d=wi*7+1/2 alpha t^2
where wi is the angular rotation at the end of the first four seconds. I can't find the post which I need to put a number on it, but as I recall, you had an angular acceleration for a time period to get that wf, now a wi.

Answer 2

The angular velocity after 4s is 15r/s

so would it be
15(7) + .5(3.75)(49) = 196.875?

Answer 3

It is! Thanks for your help