O is the centre of a circle. AC and BD are two chords of the circle intersecting each other at P, If `angleAOB =15^@ and angle APB = 30^@,` then `angle COD` is equal to

Answer

To solve the problem, we need to find the value of angle COD given the angles AOB and APB. Let's break it down step by step.

### Step-by-Step Solution:

1. **Identify the Given Angles:**
- We have angle AOB = 15°.
- We have angle APB = 30°.

2. **Use the Angle Relationship:**
- According to the properties of intersecting chords in a circle, the following relationship holds:
\[ \text{Angle AOB} + \text{Angle COD} = 2 \times \text{Angle APB} \]
- This means that:
\[ 15° + \text{Angle COD} = 2 \times 30° \]

3. **Calculate the Right Side:**
- Calculate \(2 \times 30°\):
\[ 2 \times 30° = 60° \]

4. **Set Up the Equation:**
- Now we can set up the equation:
\[ 15° + \text{Angle COD} = 60° \]

5. **Solve for Angle COD:**
- To find Angle COD, subtract 15° from both sides:
\[ \text{Angle COD} = 60° - 15° \]
- Therefore:
\[ \text{Angle COD} = 45° \]

### Final Answer:
Angle COD is equal to 45°.

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