NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 2: Geometry - Problems and Solutions

Question 51

Think of the two angles placed next to each other at point B.

1. Both angles have the same vertex: \(B\).
2. They share a common arm: \(BC\).
3. The other arms are different:
   \(\angle ABC\): from \(BA\) to \(BC\)
   \(\angle CBD\): from \(BC\) to \(BD\)
4. Such angles are called adjacent angles. When placed side by side, they form the bigger angle from \(BA\) to \(BD\): \(\angle ABD\).
5. So their measures add up step by step:
   \(\text{measure}(\angle ABC)\)
   \(+\ \text{measure}(\angle CBD)\)
   \(=\ \text{measure}(\angle ABD)\)

Therefore, adding \(\angle ABC\) and \(\angle CBD\) gives \(\angle ABD\).