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 angles

plz answer this immediately , its most urgent

  In this example, a° and b° are vertical angles.

The interesting thing here is that vertically opposite angles are equal:

 Because b° is vertically opposite 40°, it must also be 40°

A full circle is 360°, so that leaves 360° - 2×40° = 280°

Angles a° and c° are also vertically opposite, so must also be equal, which means they are 140° each.

Answer: a = 140°, b = 40° and c = 140°.