WAEC Mathematics 2014 Paper

Concept:The exterior angles form linear pairs with the interior angles of the triangle, so the angle sum property of a triangle can be used to solve for $n$.Explanation:Let the two other interior angles of the triangle be $z$ and $k$.Since $y$ and $z$ lie on a straight line, $y+z=180^\circ$, so $z=180^\circ-y$.Since $x$ and $k$ lie on a straight line, $x+k=180^\circ$, so $k=180^\circ-x$.The sum of the interior angles of the triangle is $n+z+k=180^\circ$.Substituting the expressions for $z$ and $k$ gives $n+(180^\circ-y)+(180^\circ-x)=180^\circ$.Simplify: $n+360^\circ-(x+y)=180^\circ$.Rearrange: $n+180^\circ=x+y$.Given $x+y=220^\circ$, substitute to obtain $n+180^\circ=220^\circ$.Thus, $n=220^\circ-180^\circ=40^\circ$.Answer:$n=40^\circ$, so the correct option is B.