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Lines PQ and RS cross at O, making the four numbered angles shown. Which pair of angles are vertically opposite angles?

Class 7Lines and AnglesLines and Angles
  • A∠1 and ∠2
  • B∠2 and ∠3
  • C∠3 and ∠4
  • D∠1 and ∠3

Step-by-Step Solution

Vertically opposite angles lie across the crossing point and do not share an arm. ∠1 and ∠3 face each other across O, so they are vertically opposite (and equal). ∠1 and ∠2 share the arm OR, so they form a linear pair.
Answer: D) ∠1 and ∠3

Key idea: Vertically opposite angles

When two straight lines cross, four angles form at the intersection. The two angles directly **across** the vertex (sharing only the vertex, not a side) are called **vertically opposite** — and they are always equal.

If one angle is 70°, then:
- Its vertical opposite is also 70°.
- The other two angles are each 110° (linear pair with 70°).

Why? Each pair forms a linear pair with a common neighbour, both summing to 180° — so the opposites end up equal.

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