Three rays emanate from a common point and form three angles with measure p, q , r. which one of the measure of anlge `q + r`?

Options

A. `q + r gt 180^@`
B. `q + r lt 180^@`
C. `q + r = 180^@`
D. It cannot be determined from the information given

Answer

To solve the problem, we need to analyze the situation where three rays emanate from a common point and form three angles, denoted as \( p \), \( q \), and \( r \).

### Step-by-Step Solution:

1. **Understanding the Angles**:
- Let the three rays be \( OA \), \( OB \), and \( OC \) originating from point \( O \).
- The angles formed by these rays can be represented as:
- Angle \( AOB = p \)
- Angle \( BOC = q \)
- Angle \( COA = r \)

2. **Relationship Between the Angles**:
- Since the rays are emanating from a common point, the sum of the angles around that point must equal \( 360^\circ \).
- Therefore, we can write the equation:
\[ p + q + r = 360^\circ \]

3. **Finding \( q + r \)**:
- To find the measure of angle \( q + r \), we can rearrange the equation:
\[ q + r = 360^\circ - p \]
- This shows that the sum of angles \( q \) and \( r \) depends on the measure of angle \( p \).

4. **Conclusion**:
- Since we do not have specific values for \( p \), \( q \), or \( r \), we cannot determine a specific numerical value for \( q + r \).
- Thus, the information provided is insufficient to conclude the exact measure of angle \( q + r \).

### Final Answer:
The measure of angle \( q + r \) cannot be determined with the given information.