Answer on the basis of the following statements. When two straight lines intersect, then :
adjacent angles are complementary
adjacent angles are supplementary
opposite angles are equal
opposite angles are supplementary

Options

A. 2 and 3 are correct
B. 1 and 4 are correct
C. 1 and 3 are correct
D. 2 and 4 are correct

Answer

To solve the question regarding the properties of angles formed when two straight lines intersect, we can analyze each statement provided:

1. **Adjacent angles are complementary.**
2. **Adjacent angles are supplementary.**
3. **Opposite angles are equal.**
4. **Opposite angles are supplementary.**

### Step-by-Step Solution:

**Step 1: Understand the Intersection of Lines**
When two straight lines intersect, they form four angles. Let's label these angles as Angle 1, Angle 2, Angle 3, and Angle 4.

**Step 2: Analyze Adjacent Angles**
Adjacent angles are angles that share a common side and a common vertex. For example:
- Angle 1 and Angle 2 are adjacent.
- Angle 2 and Angle 3 are adjacent.
- Angle 3 and Angle 4 are adjacent.
- Angle 4 and Angle 1 are adjacent.

**Step 3: Determine if Adjacent Angles are Complementary or Supplementary**
Adjacent angles formed by intersecting lines add up to 180 degrees. Therefore, they are supplementary. For example:
- Angle 1 + Angle 2 = 180 degrees
- Angle 2 + Angle 3 = 180 degrees
- Angle 3 + Angle 4 = 180 degrees
- Angle 4 + Angle 1 = 180 degrees

Thus, the statement "Adjacent angles are supplementary" is **correct**.

**Step 4: Analyze Opposite Angles**
Opposite angles are the angles that are across from each other when two lines intersect. For example:
- Angle 1 is opposite to Angle 4.
- Angle 2 is opposite to Angle 3.

**Step 5: Determine if Opposite Angles are Equal or Supplementary**
According to the properties of intersecting lines:
- Angle 1 = Angle 4
- Angle 2 = Angle 3

Thus, opposite angles are equal, which means the statement "Opposite angles are equal" is also **correct**.

**Step 6: Check the Last Statement**
The statement "Opposite angles are supplementary" is **incorrect** because opposite angles are equal, not supplementary.

### Conclusion:
Based on the analysis:
- **Correct Statements**:
- Adjacent angles are supplementary.
- Opposite angles are equal.

### Final Answer:
The correct statements are:
- Adjacent angles are supplementary (Statement 2).
- Opposite angles are equal (Statement 3).