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Three straight lines all pass through a single point O, so six angles are formed around O. Five of them measure 42°, 68°, 70°, 42° and 68°. Find the sixth angle.

Class 7Lines and AnglesLines and Angles
  • A80°
  • B110°
  • C70°
  • D290°

Step-by-Step Solution

Angles around a point sum to 360°, and the five given angles total 42 + 68 + 70 + 42 + 68 = 290°, so the sixth = 360 − 290 = 70°. A quicker route: three lines through O make three pairs of vertically opposite angles, and 70° is the one measure without a partner yet — so the sixth must match it. Trap: 110° is 180 − 70, which treats the missing angle as a linear-pair partner instead of closing the full turn.
Answer: C) 70°

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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