There are at least two ways to do it.
1. Rotate the coordinate system so (x,y) become (x',y'), so it become zero degree again.
And check it by the same method.

2. if the coordinates for those four points are (x1,y1), (x2,y2), (x3,y3) and (x4,y4).
Assume a line L1: $y=m_1 x+b_1$ pass (x1,y1) and (x2,y2). Then $y>m_1a+b_1$ is at the right side of the L1,  $y is at left side of L1
Another line L2: $y=m_2 x+b_2$ pass (x3,y3) and (x4,y4).

If the compass is inside, it must be between L1 and L2.
So you can find out condition (1) : $(y-m_1 x-b_1)(y-m_2 x-b_2)<0$

There are another two lines
L3 :pass (x1,y1) , (x4,y4)
L4: pass (x2,y2) , (x3,y3)
So you can find out another condition (2): $(y-m_3 x-b_3)(y-m_4 x-b_4)<0$

The compass is inside if the above two conditions are satisfied at the same time (use and operator ).