On the attached image we have three angles, d $\displaystyle \phi$ and $\displaystyle \theta$ with r2 as a side of the triangle

I know d and $\displaystyle \phi$ but I am trying to find $\displaystyle \theta$.

r2 is the normal to a surface and angle d is created by refraction. Since it is measured anti-clockwise it results in a negative angle of -19.77.

Angle $\displaystyle \phi$ is equal to 35 degrees.

The author states to determine angle $\displaystyle \theta$ you add d to $\displaystyle \phi$ and this is what I do not understand.

I would subtract 180 from (145+19.77).

Both ways give the same result, but I am trying to understand the other way