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∠XOY = 54° and ∠YOZ = 71° are adjacent angles that share the arm OY. Find ∠XOZ.

Class 7Lines and AnglesLines and Angles
  • A125°
  • B17°
  • C55°
  • D235°

Step-by-Step Solution

Adjacent angles sit side by side with no overlap, so the whole angle is simply their sum: ∠XOZ = 54 + 71 = 125°. Trap: 17° is the difference, which would only matter if OY lay outside ∠XOZ; 55° is 180 − 125, treating this as a linear pair even though the two angles do not add to 180°.
Answer: A) 125°

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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