WAEC 2024 · Paper 1 · Q31

Circle geometry

In the diagram, $JKL$ is a tangent to the circle $GHIK$ at $K$ . $\angle LKG = 38^\circ$ and $\angle HIK = 87^\circ$ . Calculate the value of the angle marked $x$ .

The paper marks this diagram “not drawn to scale”; the redraw uses the true measurements.

Worked solution (try it first)

$HIKG$ is a cyclic quadrilateral, so opposite angles add up to $180^\circ$ : $\angle HGK = 180^\circ - 87^\circ$
$= 93^\circ$ .
$H$ , $G$ and $L$ are on a straight line, so $\angle KGL = 180^\circ - 93^\circ$
$= 87^\circ$ .
The angles of triangle $KGL$ add up to $180^\circ$ : $x = 180^\circ - 38^\circ - 87^\circ$
$= 55^\circ$ , option B.

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