NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 2: Geometry - Problems and Solutions
Question 54

Question. 54

Look at Fig. 2.34. Mark (a) a point A which is in the interior of both ∠1 and ∠2; (b) a point B which is in the interior of only ∠1; (c) a point C in the interior of ∠1. Now state whether points B and C lie in the interior of ∠2 also.

Answer:

One possible marking (as in the figure): A lies inside both ∠1 and ∠2; B lies inside only ∠1; C lies inside ∠1.

Thus, B is not in ∠2; C is not in ∠2.

Detailed Answer with Explanation:

Follow these simple checks.

  1. Meaning of interior: A point is in the interior of an angle if it lies between the two arms of that angle (not on the arms).
  2. Point A: Place A in the region where ∠1 and ∠2 overlap. So A is inside both ∠1 and ∠2.
  3. Point B: Place B in the region that belongs to ∠1 but is outside ∠2. Then B is inside ∠1 only.
  4. Point C: Place C anywhere else inside ∠1. In the given figure, this spot is outside ∠2.
  5. Conclusion: A is in both ∠1 and ∠2. B is not in ∠2. C is not in ∠2.

Note: If a point lies on an arm, it is not counted as interior.

Open NCERT PDF