Which of the following could be the four angles of a parallelogram?
(I) `50^@, 130^(@), 50^@, 130^@`
(II) `125^@, 50^@, 125^@, 60^@`

Options

A. I only
B. II only
C. I and II only
D. None of them

Answer

To determine which of the given sets of angles could represent the angles of a parallelogram, we need to recall the properties of a parallelogram. In a parallelogram, opposite angles are equal, and the sum of the angles in any quadrilateral is 360 degrees.

Let's analyze the options step by step.

### Step 1: Analyze the first option
The first option gives us the angles: \(50^\circ, 130^\circ, 50^\circ, 130^\circ\).

- **Check for opposite angles:**
- Angle A = \(50^\circ\) and Angle C = \(50^\circ\) (opposite angles)
- Angle B = \(130^\circ\) and Angle D = \(130^\circ\) (opposite angles)

- **Check the sum of angles:**
\[ 50^\circ + 130^\circ + 50^\circ + 130^\circ = 360^\circ \]

Since both conditions are satisfied (opposite angles are equal and the sum of angles is \(360^\circ\)), the first option is valid.

### Step 2: Analyze the second option
The second option gives us the angles: \(125^\circ, 50^\circ, 125^\circ, 60^\circ\).

- **Check for opposite angles:**
- Angle A = \(125^\circ\) and Angle C = \(125^\circ\) (opposite angles)
- Angle B = \(50^\circ\) and Angle D = \(60^\circ\) (not equal)

Since the opposite angles are not equal (Angle B and Angle D), this option does not satisfy the properties of a parallelogram.

### Conclusion
Based on the analysis:
- The first option \(50^\circ, 130^\circ, 50^\circ, 130^\circ\) is valid.
- The second option \(125^\circ, 50^\circ, 125^\circ, 60^\circ\) is not valid.

Thus, the correct answer is that only the first option could represent the angles of a parallelogram.