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Lines AB and CD cross at O. ∠AOC = ° and ∠BOD = ° are vertically opposite. Find ∠AOC.

Class 7Lines and AnglesLines and Angles
  • A20°
  • B86°
  • C94°
  • D76°

Step-by-Step Solution

Vertically opposite angles are equal, so → → . Then ∠AOC = °, and ° confirms it. Trap: 20° is the value of , not the angle; 94° is 180 − 86, which comes from confusing vertically opposite angles with a linear pair.
Answer: B) 86°

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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