WAEC 2021 · Paper 1 · Q39

In the diagram, $EC$ is a diameter of the circle. If $\angle ABC = 158^\circ$ , find $\angle ADE$ .

Worked solution (try it first)

$ABCE$ is a cyclic quadrilateral, so $\angle AEC = 180^\circ - 158^\circ$
$= 22^\circ$ .
$EC$ is a diameter, so $\angle EAC = 90^\circ$ .
In triangle $EAC$ , $\angle ACE = 180^\circ - 90^\circ - 22^\circ$
$= 68^\circ$ .
Angles in the same segment: $\angle ADE$ and $\angle ACE$ both stand on arc $AE$ , so $\angle ADE = 68^\circ$ , option C.