Mathematics

Problem

Draw two straight lines

PQ

and

RS

intersecting at

O

. a. (i) Prove that the vertically opposite angles formed at

O

are equal. b. (ii) If

\angle POQ=2a

and

\angle ROS=5a-45^\circ

, use the result of part (i) to find the value of

a

and the measure of each of the four angles at

O

. State each reason clearly in your working.