WAEC Mathematics 2010 Paper

Concept:Use corresponding angles from parallel lines and equal base angles of an isosceles triangle, then apply the straight-line angle sum.Explanation:Since $QR \parallel ST$, the corresponding angles formed by transversal $PS$ are equal.So $\angle PQR = \angle PST = 75^\circ$.Given $PQ = PR$, triangle $PQR$ is isosceles.Therefore, base angles are equal:$\angle PRQ = \angle PQR = 75^\circ$.At point $R$, the marked angle $y$ and $\angle PRQ$ lie on a straight line.Thus, $y + 75^\circ = 180^\circ$.So $y = 180^\circ - 75^\circ = 105^\circ$.Answer:$y = 105^\circ$ $\Rightarrow$ Option A.