Using ruler and compasses only, draw a right angle.

Hint: To start with, we need to draw a reference line AB, with respect to which the required right angle will be drawn. Then, choosing any of the two points, say A, as centre and opening the compass to a suitable radius, we have to draw an arc cutting AB at C. With the same radius and C as centre, we will draw an arc cutting the original arc at D. Then, with the same radius and D as centre, we will draw an arc cutting the original arc at E. Then consecutively choosing D and E as centers and the same radius, we will draw two arcs cutting each other at F. Finally, we will join the points A and F so that the angle FAB will be the required right angle.

Complete step by step solution:
Step I: Draw a base line segment AB

Step II: Choosing A as centre and a convenient radius, draw an arc which cuts AB at C.

Step III: Now, taking C as centre and the same radius, draw an arc cutting the original arc at point D.

Step IV: Now, taking D as centre and with the same radius, draw an arc cutting the original arc at E.

Step V: Taking D as centre and the same radius, draw an arc.

Step VI: Similarly, taking E as centre and the same radius, draw an arc cutting the previous arc at F.

Step VII: Finally, join the points A and F.

Hence, the angle FAB is the required right angle.

Note: As we can notice in the above solution, the radius is not changed in any of the steps. Therefore, we must be careful while choosing the radius and it must be less than the length of AB. Also, the arcs must be drawn very lightly so as to accurately obtain the final right angle.