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Lines AB and CD intersect at O, and ∠AOC = 47°. Find ∠BOC + ∠AOD.

Class 7Lines and AnglesLines and Angles
  • A266°
  • B133°
  • C313°
  • D180°

Step-by-Step Solution

∠BOC forms a linear pair with ∠AOC, so ∠BOC = 180 − 47 = 133°. ∠AOD also forms a linear pair with ∠AOC, so ∠AOD = 133° too (they are vertically opposite each other). Sum = 133 + 133 = 266°. Trap: 133° is only one of the two angles; 180° comes from assuming ∠BOC and ∠AOD form a linear pair with each other — they do not, they are vertically opposite and therefore equal.
Answer: A) 266°

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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