Draw two straight lines and intersecting at .

MATHEMATICS · Multi-part · CBSE · Mathematics · Lines and Angles · Lines and Angles

Problem

Draw two straight lines

PQ

and

RS

intersecting at

O

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

O

are equal. (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.