https://file.aiquickdraw.com/mathbot/file/1726720707650s00jhti7.jpg

To determine whether each statement can be assumed from the figure, we first need to understand what a linear pair is. A **linear pair** of angles consists of two adjacent angles whose non-common sides form a straight line. The sum of the angles in a linear pair is always \( 180^\circ \).

In this case, we are analyzing the angles \( \angle SRQ \) and \( \angle QRP \), which are said to form a linear pair according to the figure.

- **\( \angle SRQ \)** is the angle formed by lines \( SR \) and \( RQ \).
- **\( \angle QRP \)** is the angle formed by lines \( RQ \) and \( QP \).

Since these angles form a linear pair, their sum must be \( 180^\circ \), and the correct statement is:

### A. **Yes, their sum is 180.**

- **B** (Yes, their sum is 90) is incorrect because linear pairs do not sum to \( 90^\circ \); they sum to \( 180^\circ \).
- **C** (No, their sum is 360) is also incorrect because linear pairs cannot sum to \( 360^\circ \), only angles around a point (full rotation) sum to \( 360^\circ \).
- **D** (No, their sum cannot be determined) is incorrect because the diagram clearly shows that they form a linear pair, allowing us to determine their sum as \( 180^\circ \).

Would you like further details or have any other questions about this?

Here are five related questions to explore:
1. What is a supplementary angle, and how does it differ from a linear pair?
2. How do adjacent angles differ from vertical angles?
3. Can two angles form a linear pair if they are not adjacent?
4. What is the definition of a straight angle, and how does it relate to a linear pair?
5. How do we calculate the sum of interior angles in different polygons?

**Tip:** In any geometry problem involving lines and angles, looking for linear pairs or vertically opposite angles is often a good strategy for simplifying calculations.

Determine whether each statement can be assumed from the figure, considering that ∠SRQ and ∠QRP is a linear pair. Explain if their sum is 180, 90, 360, or cannot be determined.

Explore how to determine the sum of angles in a linear pair. Learn about ∠SRQ and ∠QRP, and why their sum is 180° based on the Linear Pair Theorem. This problem covers key geometry concepts and is suitable for students in Grades 7-9.

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