NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 2: Geometry - Multiple Choice Questions

Question 8

Beginner-friendly steps

1. In the figure, four rays meet at one point (the vertex). Name them in order as OA, OB, OC, OD.
2. The small adjacent angles between these rays are given as:
   \(\angle AOB = 40^{\circ}\)
   \(\angle BOC = 30^{\circ}\)
   \(\angle COD = 20^{\circ}\)
3. Every pair of adjacent small angles makes a bigger angle. Add them:
   \(\angle AOC = \angle AOB + \angle BOC = 40^{\circ} + 30^{\circ} = 70^{\circ}\)
   \(\angle BOD = \angle BOC + \angle COD = 30^{\circ} + 20^{\circ} = 50^{\circ}\)
4. All three small angles together also make one angle:
   \(\angle AOD = \angle AOB + \angle BOC + \angle COD = 40^{\circ} + 30^{\circ} + 20^{\circ} = 90^{\circ}\)
5. Now count all distinct angles formed at the vertex:
   Small: \(\angle AOB\), \(\angle BOC\), \(\angle COD\) → 3 angles
   Combined: \(\angle AOC\), \(\angle BOD\), \(\angle AOD\) → 3 angles
   Total = \(3 + 3 = 6\)

Answer: Option D — 6 angles.