Fill in the blanks and select the correct option.
(i) If two lines intersect each other, then the vertically opposite angles are ____(P)
(ii) The angles of a linear pair are _____(Q) as well as ____(R)
(iii) If a transversal is perpendicular to two parallel lines then sum of each pair of corresponding angles is ______(S)

Options

A. `{:(P,Q,R,S),("Unequal","adjacent","complementary",90^(@)):}`
B. `{:(P,Q,R,S),("Unequal","complementary","supplementary",90^(@)):}`
C. `{:(P,Q,R,S),("Equal","adjacent","supplementary",180^(@)):}`
D. `{:(P,Q,R,S),("Equal","supplementary","complementary",180^(@)):}`

Answer

Let's solve the question step by step:

### Step 1: Understanding Vertically Opposite Angles
When two lines intersect, they form four angles. The angles that are opposite each other at the intersection point are called vertically opposite angles.

**Fill in the blank:** If two lines intersect each other, then the vertically opposite angles are **equal**.

### Step 2: Understanding Angles of a Linear Pair
A linear pair consists of two adjacent angles formed when two lines intersect. The sum of the angles in a linear pair is always 180 degrees because they form a straight line.

**Fill in the blanks:** The angles of a linear pair are **adjacent** as well as **supplementary**.

### Step 3: Understanding Corresponding Angles with a Transversal
When a transversal intersects two parallel lines, it creates pairs of corresponding angles. If the transversal is perpendicular to both parallel lines, each corresponding angle will measure 90 degrees.

**Fill in the blank:** If a transversal is perpendicular to two parallel lines, then the sum of each pair of corresponding angles is **180 degrees**.

### Final Answers:
(i) **equal** (P)
(ii) **adjacent** (Q) as well as **supplementary** (R)
(iii) **180 degrees** (S)

### Summary of Answers:
- P: equal
- Q: adjacent
- R: supplementary
- S: 180 degrees