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The worksheet you're working on involves logic statements related to geometry. Specifically, it deals with conditional statements and their variations: converse, inverse, and contrapositive. Let's break down the content:

### Conditional Statement:
- **Given Statement (P → Q)**: "If an angle is obtuse, then it measures 137°."
  - **P**: "An angle is obtuse."
  - **Q**: "The angle measures 137°."

### Converse Statement (Q → P):
- **Q → P**: "If it measures 137°, then the angle is obtuse."
  - The truth of this statement depends on whether the angle measuring 137° always makes it obtuse, which is true because obtuse angles are angles greater than 90° and less than 180°, and 137° fits in this range. Therefore, the converse statement is **True**.

### Inverse Statement (¬P → ¬Q):
- **¬P → ¬Q**: "If an angle is not obtuse, then it does not measure 137°."
  - This statement implies that only obtuse angles can measure 137°, which is correct, because non-obtuse angles are either acute or right, and neither of them can measure 137°. Thus, the inverse statement is **True**.

### Contrapositive Statement (¬Q → ¬P):
- **¬Q → ¬P**: "If it does not measure 137°, then the angle is not obtuse."
  - This statement is logically equivalent to the original conditional statement. If the angle doesn’t measure 137°, it does not necessarily mean that the angle isn’t obtuse (e.g., an angle measuring 120° is still obtuse). So this statement would be **False**.

### Truth Values:
- Conditional Statement (P → Q): False (Not all obtuse angles measure exactly 137°).
- Converse Statement (Q → P): True (An angle measuring 137° is obtuse).
- Inverse Statement (¬P → ¬Q): True (An angle not obtuse cannot be 137°).
- Contrapositive Statement (¬Q → ¬P): False (Not all obtuse angles must measure exactly 137°).

Let me know if you need further clarification or have additional questions! Here are some related questions to deepen your understanding:

1. What is a biconditional statement, and can it apply to this example?
2. Can an acute angle ever have a converse, inverse, or contrapositive like the ones listed here?
3. How would the truth values change if the original conditional statement were about a right angle instead?
4. How can you generalize the contrapositive of a conditional statement?
5. How does the contrapositive compare to the converse in logical structure?

**Tip:** Remember, the contrapositive of a statement is always logically equivalent to the original statement!

Given a conditional statement about an angle being obtuse and measuring 137°, analyze the converse, inverse, and contrapositive of the statement and determine their truth values.

Learn how to analyze a conditional statement about an obtuse angle and its measurement using the converse, inverse, and contrapositive. Explore the truth values of each statement and understand their significance in logical reasoning. Suitable for Grades 8-10 geometry students.

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