Step 1: Evil genius hypothesis
Descartes imagined an "evil genius" who could deceive him even in matters of logic and mathematics. This radical doubt extended not only to sensory experience but also to apparently indubitable truths like arithmetic.
Step 2: Apply to the statements
- (II) "The sum of the angles of a triangle is 180 degrees" → A mathematical truth. Under the evil genius hypothesis, even such truths could be doubted.
- (VIII) "2+2=4" → The simplest arithmetic truth, yet Descartes shows that the evil genius could make us doubt even this.
- Other statements (I, III, IV, V, VI, VII) relate to empirical observation or personal states, not Descartes' focus in the evil genius argument.
Step 3: Conclusion
Therefore, Descartes' evil genius mainly denies certainty of mathematical/logical truths, i.e., (II) and (VIII).
\[
\boxed{\text{Correct Answer: (D) II and VIII}}
\]