ABCD is a cyclic parallelogram. The angle `/_B` is equal to :

Options

A. `30^@`
B. `60^@`
C. `45^@`
D. `90^@`

Answer

To solve the problem of finding the angle \( \angle B \) in the cyclic parallelogram \( ABCD \), we can follow these steps:

### Step 1: Understand the Properties of a Cyclic Parallelogram
A cyclic parallelogram is a quadrilateral that is both a parallelogram and inscribed in a circle. This means that all its vertices lie on the circumference of the circle.

**Hint:** Recall that a cyclic quadrilateral has specific properties related to its angles.

### Step 2: Identify the Properties of a Parallelogram
In a parallelogram, opposite sides are equal, and opposite angles are equal. Therefore, we have:
- \( AB = CD \)
- \( AD = BC \)
- \( \angle A = \angle C \)
- \( \angle B = \angle D \)

**Hint:** Remember that in a parallelogram, opposite angles are equal.

### Step 3: Use the Property of Cyclic Quadrilaterals
For any cyclic quadrilateral, the sum of opposite angles is \( 180^\circ \). Thus, we can write:
\[ \angle A + \angle C = 180^\circ \]
Since \( \angle A = \angle C \), we can substitute:
\[ \angle B + \angle D = 180^\circ \]

**Hint:** Use the property of cyclic quadrilaterals to relate the angles.

### Step 4: Substitute the Equal Angles
Since \( \angle B = \angle D \) (as established from the properties of the parallelogram), we can substitute \( \angle D \) with \( \angle B \):
\[ \angle B + \angle B = 180^\circ \]
This simplifies to:
\[ 2\angle B = 180^\circ \]

**Hint:** Combine like terms to simplify the equation.

### Step 5: Solve for \( \angle B \)
Now, divide both sides by 2 to find \( \angle B \):
\[ \angle B = \frac{180^\circ}{2} = 90^\circ \]

**Hint:** Perform the final calculation to find the measure of the angle.

### Conclusion
Thus, the angle \( \angle B \) in the cyclic parallelogram \( ABCD \) is \( 90^\circ \).

**Final Answer:** \( \angle B = 90^\circ \)