Which of the following statement(s) is/are correct?

Options

A. A parallelogram in which two adjacent angles are equal is a rectangle.
B. A quadrilateral in which both pairs of opposite angles are equal is a parallelogram.
C. In a parallelogram, the maximum number of acute angles can be two.
D. All of these

Answer

To determine which of the statements about parallelograms is correct, we will analyze the statements step by step.

### Step 1: Understand the Properties of a Parallelogram
A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length. The opposite angles are also equal, and the sum of the interior angles is always 360 degrees.

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

### Step 2: Analyze the First Statement
The first statement claims that "a parallelogram in which two adjacent angles are equal is a rectangle."

- If two adjacent angles of a parallelogram are equal, let's denote them as angle A and angle B. Since the sum of angles A and B must equal 180 degrees (because they are adjacent), if angle A = angle B, then each angle must be 90 degrees.
- Therefore, if two adjacent angles are equal, it implies that each angle is 90 degrees, making the parallelogram a rectangle.

**Hint:** Check if the equality of adjacent angles leads to each being 90 degrees.

### Step 3: Analyze the Second Statement
The second statement claims that "the two opposite angles of the two angles are equal."

- In a parallelogram, it is a known property that opposite angles are always equal. So if we have angle A and angle C as opposite angles, then angle A = angle C, which confirms this statement.

**Hint:** Recall that in any parallelogram, opposite angles are always equal.

### Conclusion
Based on the analysis:
- The first statement is **correct** because it correctly describes the condition under which a parallelogram becomes a rectangle.
- The second statement is also **correct** because it states a fundamental property of parallelograms.

### Final Answer
Both statements are correct.