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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.

Identify two statements that contradict each other from the following: I. ∠M is an obtuse angle, II. m∠M + m∠P = 90°, III. 180° - m∠M = 25°, IV. m∠P = 120°.

Learn how to identify contradictory statements in an angle problem involving obtuse and complementary angles. This problem covers the properties of obtuse angles, complementary angles, and their sum relationships. Suitable for students in Grades 7-9.

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