Question

In the adjoining figure, three coplanar lines AB, CD and EF intersect at a point O, forming angles as shown. Find the values of x, y, z and t.

Answer 1

We know that if two lines intersect, then the vertically opposite angles are equal.
$\therefore \angle BOD=\angle AOC=90°$
Hence, $t=90°$
Also,
$\angle DOF=\angle COE=50°$
Hence, $z=50°$
Since, AOB is a straight line, we have:
$$\begin{gathered} \angle AOC+\angle COE+\angle BOE=180° \\ \Rightarrow 90+50+y=180° \\ \Rightarrow 140+y=180° \\ \Rightarrow y=40° \end{gathered}$$
Also,
$\angle BOE=\angle AOF=40°$
Hence, $x=40°$
$\therefore x=40°,y=40°,z=50°\text{and}t=90°$