NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 9: Symmetry and Practical Geometry - True or False Questions

Question 53

Yes — the statement is true.

Idea: We have two set-squares in the geometry box:

• One is 45°–45°–90°
• The other is 30°–60°–90°

Using these, we can make an angle of (15^circ) because:

Construction (easy steps):

1. Draw a base ray (overrightarrow{OA}) with a ruler.
2. Place the 60° set-square so that one short side lies along (overrightarrow{OA}). Draw the ray (overrightarrow{OC}) making (60^circ) at (O).

   (angle AOC = 60^circ)

3. Without moving point (O), place the 45° set-square with one short side again along (overrightarrow{OA}). Draw the ray (overrightarrow{OB}) making (45^circ) at (O).

   (angle AOB = 45^circ)

4. Now look at the small angle between the two new rays (overrightarrow{OB}) and (overrightarrow{OC}). That angle is:

   (angle BOC = 60^circ - 45^circ = 15^circ)

Conclusion: By drawing (60^circ) and (45^circ) from the same point, the small angle between them is exactly (15^circ). So an angle of (15^circ) can be constructed using only the two set-squares.

Tip (if you need a single ray at (15^circ) from the base): Place the 45° set-square with one edge along (overrightarrow{OA}), then slide/align the 60° set-square so that one of its edges passes through the 45° line at point (O). The edge that lies between the 45° and 60° positions gives you the (15^circ) ray from the base.