WAEC Mathematics 2018 Paper

Concept:Use alternate angles, the straight-line angle sum, and the exterior angle theorem of a triangle.Explanation:Since $PQ \parallel RS$, mark the angle alternate to $z$ as $a$.Therefore, $a = z$.Angles $a$ and $b$ lie on a straight line, so:$a + b = 180^\circ$Hence, $b = 180^\circ - z$.Angles $x$ and $c$ also lie on a straight line, so:$c = 180^\circ - x$Angle $y$ is the exterior angle of the triangle, so it equals the sum of the opposite interior angles $b$ and $c$.Thus, $y = b + c$.Substitute the values:$y = (180^\circ - z) + (180^\circ - x)$$y = 360^\circ - x - z$Rearrange to express $x$ in terms of $y$ and $z$:$x = 360^\circ - y - z$Answer:$x = 360^\circ - y - z$So the correct option is D.