If a Quardlateral is circumscribed of a circle and `angle AOB ` is ` 135^(@)` find angle COD . O is the centre of circle

Answer

To solve the problem, we need to find the angle \( \angle COD \) given that \( \angle AOB = 135^\circ \) and that the quadrilateral \( ABCD \) is circumscribed about a circle.

### Step-by-Step Solution:

1. **Understanding the Properties of the Quadrilateral**:
A quadrilateral that can be circumscribed about a circle has a special property: the sum of the angles subtended by opposite sides at the center of the circle is equal to \( 180^\circ \). This means:
\[ \angle AOB + \angle COD = 180^\circ \]

2. **Substituting the Given Angle**:
We know that \( \angle AOB = 135^\circ \). We can substitute this value into the equation:
\[ 135^\circ + \angle COD = 180^\circ \]

3. **Isolating \( \angle COD \)**:
To find \( \angle COD \), we need to isolate it on one side of the equation. We can do this by subtracting \( 135^\circ \) from both sides:
\[ \angle COD = 180^\circ - 135^\circ \]

4. **Calculating \( \angle COD \)**:
Now, we perform the subtraction:
\[ \angle COD = 45^\circ \]

Thus, the measure of angle \( COD \) is \( 45^\circ \).

### Final Answer:
\[ \angle COD = 45^\circ \]