In the adjoining figure , ` angle AOC = 110 ^(@) , ` Calculate :
` angle ADC `

Answer

To solve for angle ADC given that angle AOC = 110°, we can use the property of angles in a circle. Here’s a step-by-step solution:

### Step-by-Step Solution:

1. **Identify the Given Information**:
- We know that angle AOC = 110°.

2. **Understand the Relationship**:
- According to the theorem of circles, the angle subtended at the center of the circle (angle AOC) is twice the angle subtended at any point on the circumference (angle ADC). This can be expressed as:
\[ \text{angle AOC} = 2 \times \text{angle ADC} \]

3. **Set Up the Equation**:
- Using the relationship from step 2, we can set up the equation:
\[ 110° = 2 \times \text{angle ADC} \]

4. **Solve for angle ADC**:
- To find angle ADC, divide both sides of the equation by 2:
\[ \text{angle ADC} = \frac{110°}{2} = 55° \]

5. **Conclusion**:
- Therefore, angle ADC = 55°.

### Final Answer:
Angle ADC = 55°

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