In Fig. 8.59, find the value of x.

In Fig. 8.57, three coplanar lines intersect at a point O, forming angles as shown in the figure, Find the values of x, y, z and u.

In Fig. 8.58, find the values of x, y and z.

Prove that the bisectors of a pair of vertically opposite angles are in the same straight line.

If two straight lines intersect each other, prove that the ray opposite to the bisector of one of the angles thus formed bisects the vertically opposite angle.