If the arms of one angle are respectively parallel to the arms of another angle , then the two angles are :

Options

A. neither equal nor supplementary
B. not equal but supplementary
C. equal but not supplementary
D. either equal or supplementary

Answer

To solve the question: "If the arms of one angle are respectively parallel to the arms of another angle, then the two angles are:", we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Angles and Lines**:
- Let’s denote the two angles as Angle A and Angle B.
- Assume the arms of Angle A are represented by two lines, say line m and line n, and the arms of Angle B are represented by two other lines that are parallel to m and n.

**Hint**: Visualize the angles and their arms as lines on a diagram to better understand their relationships.

2. **Identifying the Transversal**:
- When two lines are parallel, and a transversal line intersects them, it creates corresponding angles.
- In our case, if we have a transversal line intersecting both sets of parallel lines (m and n for Angle A, and the parallel lines for Angle B), we can analyze the angles formed.

**Hint**: Draw a diagram with parallel lines and a transversal to see how the angles are formed.

3. **Analyzing Corresponding Angles**:
- According to the properties of parallel lines and transversals, corresponding angles are equal.
- Therefore, if one arm of Angle A is parallel to one arm of Angle B, the angles formed will be equal.

**Hint**: Recall that corresponding angles formed by a transversal with parallel lines are always equal.

4. **Checking the Options**:
- The options provided in the question are:
1. Neither equal nor supplementary.
2. Not equal but supplementary.
3. Equal but not supplementary.
4. Either equal or supplementary.
- Since we established that the angles are equal, we can eliminate options 1 and 2.

**Hint**: Compare the properties of the angles with the options given to find the correct answer.

5. **Conclusion**:
- Since the angles are equal, they cannot be supplementary unless they are both 90 degrees. However, they are not necessarily supplementary in all cases.
- Therefore, the correct conclusion is that the two angles are equal.

**Hint**: Remember that angles can be equal without being supplementary unless specified otherwise.

### Final Answer:
The two angles are **equal**.