Angle B of a parallelogram ABCD is `60^(@)`, the other angles are in the ratio `A:C:D` as

Options

A. `1:2:1`
B. `2:1:3`
C. `1:2:3`
D. `2:2:1`

Answer

To solve the problem, we need to determine the angles A, C, and D of the parallelogram ABCD, given that angle B is 60 degrees and the angles are in the ratio A:C:D.

### Step-by-Step Solution:

1. **Identify the properties of the parallelogram:**
- In a parallelogram, opposite angles are equal.
- Adjacent angles are supplementary, meaning they add up to 180 degrees.

2. **Given values:**
- Angle B = 60 degrees.
- Therefore, angle D (which is opposite to angle B) = 60 degrees.

3. **Use the supplementary angle property:**
- Since angles A and B are adjacent, we can write:
\[ A + B = 180^\circ \]
- Substituting the value of angle B:
\[ A + 60^\circ = 180^\circ \]
- Solving for angle A:
\[ A = 180^\circ - 60^\circ = 120^\circ \]

4. **Determine angle C:**
- Since angle C is opposite to angle A, we have:
\[ C = A = 120^\circ \]

5. **Summarize the angles:**
- Angle A = 120 degrees
- Angle B = 60 degrees
- Angle C = 120 degrees
- Angle D = 60 degrees

6. **Express the angles in ratio form:**
- The angles A, C, and D can be expressed as:
\[ A : C : D = 120 : 120 : 60 \]

7. **Simplify the ratio:**
- Divide each term by 60:
\[ A : C : D = \frac{120}{60} : \frac{120}{60} : \frac{60}{60} = 2 : 2 : 1 \]

### Final Answer:
The angles A, C, and D are in the ratio **2 : 2 : 1**.