WAEC 2021 · Paper 1 · Q36

Circle geometry

In the cyclic quadrilateral $PQRS$ , $\angle P = \angle S = x^\circ$ , $\angle Q = (2y - 30)^\circ$ and $\angle R = (x + y)^\circ$ . Find the value of $x$ .

Worked solution (try it first)

Opposite angles of a cyclic quadrilateral add up to $180^\circ$ .
$P$ and $R$ : $x + (x + y) = 180$ , so $2x + y = 180$ .
$Q$ and $S$ : $(2y - 30) + x = 180$ , so $x + 2y = 210$ .
Double the first equation, $4x + 2y = 360$ , and take away the second: $3x = 150$ , so $x = 50$ (and $y = 80$ ).
That is option A.

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