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∠AOB = 40° and ∠BOC = 50° are adjacent angles sharing the arm OB. Do OA and OC lie in a straight line?

Class 7Lines and AnglesLines and Angles
  • AYes — adjacent angles always place their outer arms in a straight line.
  • BYes — 40 + 50 = 90°, which is a straight angle.
  • CNo — 40 + 50 = 90°, so OA and OC form a right angle, not a straight line.
  • DIt cannot be decided without seeing the figure.

Step-by-Step Solution

The outer arms form a straight line only when the two adjacent angles make a linear pair, that is when they sum to 180°. Here ∠AOC = 40 + 50 = 90°, a right angle, so OA and OC are perpendicular, not in line. Trap: being adjacent is not enough — adjacent angles need not be supplementary. Also 90° is a RIGHT angle; a straight angle is 180°.
Answer: C) No — 40 + 50 = 90°, so OA and OC form a right angle, not a straight line.

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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