Diagonals of a quadrilateral bisect each other. If `angle A = 45^(@)`, then `angle` B equals

Options

A. `45^(@)`
B. `55^(@)`
C. `135^(@)`
D. `115^(@)`

Answer

To solve the problem step by step, we will use the properties of a parallelogram since the diagonals of the quadrilateral bisect each other.

### Step-by-Step Solution:

1. **Understanding the Problem**: We are given a quadrilateral where the diagonals bisect each other, and we know that angle A = 45°. We need to find the measure of angle B.

2. **Identify the Shape**: Since the diagonals of the quadrilateral bisect each other, we can conclude that the quadrilateral is a parallelogram. This is a key property of parallelograms.

3. **Properties of Parallelograms**: In a parallelogram, adjacent angles are supplementary. This means that the sum of the measures of angle A and angle B is equal to 180°.

\[ \text{Angle A} + \text{Angle B} = 180° \]

4. **Substituting the Known Value**: We know that angle A = 45°. We can substitute this value into the equation:

\[ 45° + \text{Angle B} = 180° \]

5. **Solving for Angle B**: To find angle B, we will isolate it by subtracting 45° from both sides of the equation:

\[ \text{Angle B} = 180° - 45° \]

\[ \text{Angle B} = 135° \]

6. **Final Answer**: Therefore, the measure of angle B is 135°.

### Summary:
The measure of angle B is 135°.

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