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Assertion (A): Vertically opposite angles are always equal. Reason (R): Each of them forms a linear pair with the same neighbouring angle. Which is correct?

Class 7Lines and AnglesLines and Angles
  • ABoth A and R are true, and R correctly explains A.
  • BBoth A and R are true, but R does not explain A.
  • CA is true but R is false.
  • DA is false but R is true.

Step-by-Step Solution

Vertically opposite angles are equal. Each forms a linear pair with a common neighbour summing to 180°, which forces the opposites to be equal — so R correctly explains A.
Answer: A) Both A and R are true, and R correctly explains A.

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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