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Which of these pairs of angle measures CANNOT form a linear pair?

Class 7Lines and AnglesLines and Angles
  • A90° and 90°
  • B1° and 179°
  • C45° and 135°
  • D88° and 96°

Step-by-Step Solution

A linear pair must sum to 180°. Checking: 90 + 90 = 180, 1 + 179 = 180, 45 + 135 = 180, but 88 + 96 = 184, so that pair cannot form a linear pair. Trap: 90° and 90° looks unusual but is perfectly valid — a linear pair does not need one acute and one obtuse angle, only a sum of 180°.
Answer: D) 88° and 96°

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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