Consider the following statements: When two straight lines intersect:
(i)adjacent angles are complementary
(ii)adjacent angles are supplementary
(iii)opposite angles are equal
(iv)opposite angles are supplementary
Of those statements which is correct

Options

A. (i) and (iii) are correct
B. (ii) and (iii) are correct
C. (i) and (iv) are correct
D. (ii) and (iv) are correct

Answer

To solve the question regarding the statements about angles formed when two straight lines intersect, we can analyze each statement step by step.

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

### Step 2: Identifying Adjacent Angles
Adjacent angles are angles that share a common side and a common vertex. In our case:
- Angle 1 and Angle 2 are adjacent.
- Angle 2 and Angle 4 are adjacent.
- Angle 1 and Angle 3 are adjacent.
- Angle 3 and Angle 4 are adjacent.

### Step 3: Analyzing the First Statement
**Statement (i): Adjacent angles are complementary.**
- Complementary angles are two angles that add up to 90 degrees.
- However, adjacent angles formed by intersecting lines do not necessarily add up to 90 degrees. They actually form a linear pair, which means they add up to 180 degrees.
- **Conclusion:** This statement is **incorrect**.

### Step 4: Analyzing the Second Statement
**Statement (ii): Adjacent angles are supplementary.**
- Supplementary angles are two angles that add up to 180 degrees.
- Since adjacent angles formed by intersecting lines (like Angle 1 and Angle 2) indeed add up to 180 degrees, this statement is **correct**.

### Step 5: Analyzing the Third Statement
**Statement (iii): Opposite angles are equal.**
- Opposite angles (also known as vertically opposite angles) are formed when two lines intersect.
- According to the properties of intersecting lines, Angle 1 is equal to Angle 3, and Angle 2 is equal to Angle 4.
- **Conclusion:** This statement is **correct**.

### Step 6: Analyzing the Fourth Statement
**Statement (iv): Opposite angles are supplementary.**
- As established, opposite angles are equal, not supplementary. For example, Angle 1 and Angle 3 are equal, not adding up to 180 degrees.
- **Conclusion:** This statement is **incorrect**.

### Final Conclusion
From our analysis, the correct statements are:
- Statement (ii): Adjacent angles are supplementary.
- Statement (iii): Opposite angles are equal.

Thus, the correct options are (ii) and (iii).

### Summary of Correct Statements
- Adjacent angles are supplementary (correct).
- Opposite angles are equal (correct).
- Adjacent angles are complementary (incorrect).
- Opposite angles are supplementary (incorrect).