Two circles intersect each other at P and Q. PA and PB are two diameters. Then `angleAQB` is

Options

A. `120^(@)`
B. `135^(@)`
C. `160^(@)`
D. `180^(@)`

Answer

To solve the problem, we need to find the angle \( \angle AQB \) formed by the intersection of two circles at points \( P \) and \( Q \), where \( PA \) and \( PB \) are diameters of the respective circles.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have two circles that intersect at points \( P \) and \( Q \).
- \( PA \) and \( PB \) are diameters of the two circles.

2. **Drawing the Circles**:
- Draw two circles that intersect at points \( P \) and \( Q \).
- Mark the points \( A \) and \( B \) on the circles such that \( PA \) and \( PB \) are diameters.

3. **Identifying Angles**:
- According to the properties of circles, the angle subtended by a diameter at any point on the circumference is a right angle (90 degrees).
- Therefore, \( \angle AQP = 90^\circ \) and \( \angle BQP = 90^\circ \).

4. **Using the Angles**:
- Since both \( \angle AQP \) and \( \angle BQP \) are right angles, we can express the angle \( \angle AQB \) as the sum of these two angles:
\[ \angle AQB = \angle AQP + \angle BQP = 90^\circ + 90^\circ = 180^\circ \]

5. **Conclusion**:
- Thus, the measure of angle \( \angle AQB \) is \( 180^\circ \).

### Final Answer:
The angle \( \angle AQB \) is \( 180^\circ \).