WAEC Mathematics 2011 Paper

Concept:The solution uses the angle sum of a right triangle and the property that angles on a straight line add up to $180^\circ$.Explanation:In the first right-angled triangle, the given acute angle is $52^\circ$.The other acute angle in that triangle is therefore $90^\circ - 52^\circ = 38^\circ$.This angle is vertically opposite to the angle at $Z$, which is called $k$.Hence $k = 38^\circ$.Now consider the second right-angled triangle, where $k$ is one acute angle.The other acute angle, call it $y$, satisfies $y + k = 90^\circ$.So $y + 38^\circ = 90^\circ$, giving $y = 52^\circ$.The angle $y$ and the marked angle $x$ together form a straight line.Thus $x + y = 180^\circ$.Substitute $y = 52^\circ$ to get $x + 52^\circ = 180^\circ$.Therefore $x = 180^\circ - 52^\circ = 128^\circ$.Answer:$x = 128^\circ$, so the correct option is C.