WAEC Mathematics 2012 Paper

Concept:Use angle sums on a straight line, the angle sum of a triangle, and properties of angles formed by parallel lines $MQ \parallel RS$.Explanation:Let the angle adjacent to $\angle RLV = 30^\circ$ on the same straight line be $p$.Angles on a straight line add to $180^\circ$, so:$p + 30^\circ = 180^\circ$$p = 150^\circ$Because $MQ \parallel RS$, alternate angles are equal.So the angle inside the triangle matching the given $30^\circ$ is also $30^\circ$.In the triangle containing the $70^\circ$ angle, let the unknown angle be $k$.Using the angle sum of a triangle:$30^\circ + 70^\circ + k = 180^\circ$$k + 100^\circ = 180^\circ$$k = 80^\circ$Angles $x$ and $k$ lie on a straight line, so:$x + 80^\circ = 180^\circ$$x = 100^\circ$Answer:$x = 100^\circ$ (Option C).