The problem asks to identify two statements that contradict each other. The statements are:

I. $\angle M$ is an obtuse angle. II. $m \angle M + m \angle P = 90^\circ$. III. $180^\circ - m \angle M = 25^\circ$. IV. $m \angle P = 120^\circ$.

Let's analyze each statement:

1. Statement I says $\angle M$ is an obtuse angle, meaning $m \angle M > 90^\circ$.
2. Statement II says the sum of $m \angle M$ and $m \angle P$ is 90°. If $m \angle M$ is obtuse (greater than 90°), this would contradict this statement, as the sum would exceed 90°.
3. Statement III gives the equation $180^\circ - m \angle M = 25^\circ$, implying that $m \angle M = 155^\circ$, which makes $\angle M$ an obtuse angle. This is consistent with statement I.
4. Statement IV says $m \angle P = 120^\circ$. However, this contradicts statement II, which says the sum of $m \angle M$ and $m \angle P$ is 90°.

The two contradictory statements are II and IV because statement II requires the sum to be 90°, while statement IV says $m \angle P = 120^\circ$, which is impossible given the condition in statement II.

Thus, the correct answer is option D (III and IV).

Would you like a more detailed breakdown, or do you have any other questions?

Here are five related questions you might consider:

1. What defines an obtuse angle in geometric terms?
2. How do complementary angles relate to the sum of 90°?
3. What happens when two angles' sum exceeds 180° in a triangle?
4. How can we calculate an angle when given a sum relationship, such as in statement III?
5. How do the properties of triangle angles apply to these types of problems?

Tip: Always cross-check the sum of angles when angles are described as complementary or supplementary.