Take a line segment say AB. Make angles ${60}^{\circ }$ on both the ends such that the lines along those angles intersect at C. Taking AB as the base side, draw ${30}^{\circ }$ angle and a line along it such that it intersects AB at D. Point D bisects AB and $\angle ADB$ is ${90}^{\circ }$. So, AD is the perpendicular bisector of AB.