In cyclic quadrilateral ABCD, ` angle A = 70^(@) and angle B + angle C = 160^(@).` Then,` angle B=` ………

Options

A. `35^(@)`
B. `25^(@)`
C. `50^(@)`
D. `130^(@)`

Answer

To solve the problem, we need to find the value of angle B in the cyclic quadrilateral ABCD, given that angle A = 70° and angle B + angle C = 160°.

### Step-by-Step Solution:

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

2. **Substituting the Given Value**:
We know that angle A = 70°. Substituting this into the equation gives:
\[ 70° + \text{Angle C} = 180° \]

3. **Solving for Angle C**:
To find angle C, we can rearrange the equation:
\[ \text{Angle C} = 180° - 70° = 110° \]

4. **Using the Given Information**:
We are also given that angle B + angle C = 160°. We can substitute the value of angle C we just found:
\[ \text{Angle B} + 110° = 160° \]

5. **Solving for Angle B**:
Rearranging this equation gives:
\[ \text{Angle B} = 160° - 110° = 50° \]

### Final Answer:
Thus, the value of angle B is:
\[ \text{Angle B} = 50° \]