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Two angles forming a linear pair measure ° and °. Find the LARGER of the two angles.

Class 7Lines and AnglesLines and Angles
  • A38°
  • B78°
  • C90°
  • D102°

Step-by-Step Solution

A linear pair sums to 180°. So → → → . The angles are ° and 38 + 40 = 78°, and 102 + 78 = 180 checks out. The larger is 102°. Trap: 38° is the value of , not an angle; 78° is the smaller angle.
Answer: D) 102°

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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