NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 2: Geometry - Multiple Choice Questions
Question 7

Question.  7

In Fig. 2.7, if point A is shifted to point B along the ray PX such that PB = 2PA, then the measure of \(\angle BPY\) is

(A)

greater than 45°

(B)

45°

(C)

less than 45°

(D)

90°

Detailed Answer with Explanation:

Step-by-step:

  1. A and B lie on the same ray PX. Given \(\,PB = 2\times PA\), so B is farther from P than A.
  2. From the figure,
    \(\angle APY = 45^\circ\).
  3. Shift the point from A to B along PX (away from P). The line joining the new point to Y tilts closer to PX.
  4. Therefore the angle with PY gets smaller:
    \(\angle BPY < \angle APY\).
  5. So,
    \(\angle BPY < 45^\circ\).

Hence the measure of \(\angle BPY\) is less than 45° (Option C).

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