Question

Find the values of a and b,
Give reasons for your answers
Diagram not drawn accurately

Answer 1

$b={27}^{\circ }$ (alternate interior angles)

$\angle ABE+\angle EBD+\angle DBC={180}^{\circ }$ (angles of a straight line)

$\therefore \angle EBD={180}^{\circ }-\angle ABE-\angle DBC={180}^{\circ }-{82}^{\circ }-{27}^{\circ }={71}^{\circ }$

$\therefore \angle EBD=a^{\circ }={71}^{\circ }$ (alternate interior angles)