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Four angles meet at a point and their measures are in the ratio 2 : 3 : 4 : 6. Find the largest of the four angles.

Class 7Lines and AnglesLines and Angles
  • A96°
  • B120°
  • C144°
  • D72°

Step-by-Step Solution

Angles around a point sum to 360°. The parts total 2 + 3 + 4 + 6 = 15, so one part = 360 ÷ 15 = 24°. Largest = 6 parts = 6 (24) = 144°. Trap: 72° is what you get by dividing 180° instead of 360° among the 15 parts — but these angles go all the way round a point, not along a straight line. 96° is the second-largest angle (4 parts).
Answer: C) 144°

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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