Draw a pair of vertically opposite angles. Bisect each of the two angles. Verify that the bisecting rays are in the same line.

The steps of the required construction are:

1) Draw two intersecting line segments, intersecting at E. Taking E as center and any radius, draw a circle, intersecting the line segments at A, B, C and D. Thus ∠AEC and ∠BED are vertically opposite angles.

2) Taking A as the center draw an arc of any radius greater than . Now, Taking C as the center and the keeping the same radius, draw another arc, intersecting the previous arc at F. Join EF. Similarly, Taking B as the center draw an arc of any radius greater than . Now, Taking D as the center and the keeping the same radius, draw another arc, intersecting the previous arc at G. Join EG.

3) Measure ∠FEG using a protractor. It comes out to be 180°. Hence, FEG is a straight line.