NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 2: Geometry - Problems and Solutions
Question 51

Question. 51

Will the measure of ∠ABC and of ∠CBD make measure of ∠ABD in Fig. 2.32?

Answer:

Yes.

Detailed Answer with Explanation:

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 \(\angle ABD\).

NCERT Exemplar Solutions Class 6 – Mathematics – Unit 2: Geometry – Problems and Solutions | Detailed Answers