If a quardilateral (ABCD) is circumscribed of a circle and ∠ BOC is 125 then find ∠ AOD

Answer

To solve the problem, we need to find the angle \( \angle AOD \) in the quadrilateral \( ABCD \) that is circumscribed around a circle, given that \( \angle BOC = 125^\circ \).

### Step-by-Step Solution:

1. **Understanding the Geometry**:
- We have a quadrilateral \( ABCD \) that is circumscribed around a circle. This means that all its vertices touch the circle.
- The angles \( BOC \) and \( AOD \) are formed by the diagonals \( BD \) and \( AC \) intersecting at the center \( O \) of the circle.

2. **Using the Properties of Angles**:
- In a cyclic quadrilateral (a quadrilateral inscribed in a circle), the angles subtended by the same arc are equal.
- The angles \( \angle BOC \) and \( \angle AOD \) are related because they are both central angles that subtend the arcs \( BC \) and \( AD \) respectively.

3. **Applying the Given Information**:
- We know that \( \angle BOC = 125^\circ \).
- According to the properties of cyclic quadrilaterals, the angles \( \angle AOD \) and \( \angle BOC \) are equal.

4. **Conclusion**:
- Therefore, we can conclude that \( \angle AOD = \angle BOC = 125^\circ \).

### Final Answer:
\[ \angle AOD = 125^\circ \]