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.