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Which statement is CORRECT about a pair of vertically opposite angles?

Class 9Lines and AnglesGeometry — Lines and Angles
  • AThey are always equal in measure.
  • BThey always add up to 180°.
  • CThey always add up to 90°.
  • DThey are always adjacent angles.

Step-by-Step Solution

Vertically opposite angles (formed when two lines cross) are always equal. They are non-adjacent, not supplementary or complementary in general.
Answer: A) They are always equal in measure.

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). ✓

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