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Two straight lines cross at O. One pair of vertically opposite angles has a sum of 152°. Find the measure of each of the OTHER two angles.

Class 7Lines and AnglesLines and Angles
  • A76°
  • B152°
  • C28°
  • D104°

Step-by-Step Solution

Vertically opposite angles are equal, so each angle of the given pair is 152 ÷ 2 = 76°. Each of the other two angles forms a linear pair with a 76° angle, so each measures 180 − 76 = 104°. Trap: 76° is the pair you were given, not the pair you were asked for — the question needs one extra step.
Answer: D) 104°

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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