Practice30Create account

Assertion (A): If two lines intersect, the vertically opposite angles are equal. Reason (R): The sum of two adjacent angles formed when a ray stands on a line is 180°. Which option is correct?

Class 9Lines and AnglesGeometry — Lines and Angles
  • ABoth A and R are true, and R is the correct explanation of A.
  • BBoth A and R are true, but R is not the correct explanation of A.
  • CA is true but R is false.
  • DA is false but R is true.

Step-by-Step Solution

Vertically opposite angles are equal (A true). The linear-pair axiom (R true) is exactly the fact used to prove A: from two linear pairs we subtract the common angle to get equality. So R correctly explains A.
Answer: A) Both A and R are true, and R is the correct explanation of A.

Key idea: Linear pair and vertically opposite angles

When two straight lines intersect, four angles are formed. They satisfy two key properties:

**Linear Pair Axiom**: If a ray stands on a line, the sum of the two adjacent angles formed is **180°**.

**Vertically Opposite Angles Theorem**: When two lines cross, the angles directly opposite each other are equal.

**Quick proof of vertically opposite angles**:
Let two lines intersect, forming angles ∠1, ∠2, ∠3, ∠4 (in order around the point).
- ∠1 + ∠2 = 180° (linear pair)
- ∠2 + ∠3 = 180° (linear pair)
- So ∠1 = ∠3 (subtract ∠2 from both). ✓

Master this chapter in 30 minutes a day.

Don't just memorise the answer — build a daily practice habit.

Practice 5 Similar Questions Free →

All Lines and Angles practice questions

More Class 9 Lines and Angles practice

A transversal cuts two lines such that a pair of alternate interior angles are 50° and…Which statement is CORRECT about a pair of vertically opposite angles?Two parallel lines are cut by a transversal. One interior angle on a given side is (5x −…The angles of a triangle are (2x − 10)°, (x + 30)° and (3x + 10)°. Find the largest…Two lines are each parallel to a third line. What is the relationship between the two…