To construct a right angle, we can use the circle theorem which says that a triangle inscribed in a circle, one edge of which is a diameter, is always a right angled triangle.

Therefore, start by drawing a circle with a compass. The centre of the circle will be at the position of the compass needle.

Draw a diameter of the circle. Put the compass needle on one end of this diameter and draw an arc which crosses the circle at some point.

This point will be a vertex of the triangle. The other two vertices are the ends of the diameter. Join up the vertices. The vertex where the arc cuts the circle is the right angle.