In cyclic quadrilateral `ABCD, angle A - angle C =20^(@).` Then,`angle A=` ..........

Options

A. `20^(@)`
B. `80^(@)`
C. `100^(@)`
D. `50^(@)`

Answer

To solve the problem, we need to find the value of angle A in the cyclic quadrilateral ABCD, given that angle A - angle C = 20°.

### Step-by-Step Solution:

1. **Understand the Properties of Cyclic Quadrilaterals**:
In a cyclic quadrilateral, the sum of the opposite angles is always 180°. Therefore, we can write the following equation:
\[ \text{Angle A} + \text{Angle C} = 180° \quad \text{(Equation 1)} \]

2. **Use the Given Information**:
We are given that:
\[ \text{Angle A} - \text{Angle C} = 20° \quad \text{(Equation 2)} \]

3. **Add Equation 1 and Equation 2**:
To eliminate angle C, we can add Equation 1 and Equation 2:
\[ (\text{Angle A} + \text{Angle C}) + (\text{Angle A} - \text{Angle C}) = 180° + 20° \]
This simplifies to:
\[ 2 \cdot \text{Angle A} = 200° \]

4. **Solve for Angle A**:
Divide both sides by 2 to find angle A:
\[ \text{Angle A} = \frac{200°}{2} = 100° \]

### Final Answer:
\[ \text{Angle A} = 100° \]