In a quadrilateral `ABCD, angleA + angleC = 180^(@)`, then `angleB + angleD` is equal to

Options

A. `360^(@)`
B. `100^(@)`
C. `180^(@)`
D. `80^(@)`

Answer

To solve the problem, we need to find the sum of angles B and D in the quadrilateral ABCD given that angle A + angle C = 180 degrees.

### Step-by-Step Solution:

1. **Understanding the Quadrilateral**:
- A quadrilateral is a four-sided polygon. In this case, we have quadrilateral ABCD.

2. **Using the Angle Sum Property**:
- The sum of the interior angles of a quadrilateral is always 360 degrees. This can be expressed as:
\[ \text{Angle A} + \text{Angle B} + \text{Angle C} + \text{Angle D} = 360^\circ \]

3. **Substituting the Given Information**:
- We are given that:
\[ \text{Angle A} + \text{Angle C} = 180^\circ \]
- We can substitute this into the angle sum equation:
\[ 180^\circ + \text{Angle B} + \text{Angle D} = 360^\circ \]

4. **Isolating Angle B + Angle D**:
- To find the sum of angles B and D, we rearrange the equation:
\[ \text{Angle B} + \text{Angle D} = 360^\circ - 180^\circ \]
- Simplifying this gives:
\[ \text{Angle B} + \text{Angle D} = 180^\circ \]

5. **Conclusion**:
- Therefore, the sum of angles B and D is:
\[ \text{Angle B} + \text{Angle D} = 180^\circ \]

### Final Answer:
\[ \text{Angle B} + \text{Angle D} = 180^\circ \]