Which of the following is a correct method for constructing an angle of 60^{o} at Q?

Answer Details

The correct method for constructing an angle of 60^{o} at Q is option II only, which involves using a compass to draw an arc from point Q, cutting the line segment PQ at point R. Then, a new arc is drawn from point R, cutting the previous arc at point S. The line segment QS passing through Q and S forms a 60^{o} angle with the line segment PQ. Option I only involves bisecting an angle of 120^{o} formed by the line segments PQ and PR, which would result in an angle of 60^{o} at Q only if the original angle was 120^{o}. However, the original angle is not given in the question. Option III only involves using a ruler to measure a distance of 3 cm from Q on the line segment PQ, which would not necessarily result in an angle of 60^{o} at Q.