WAEC Mathematics 2020 Paper

Concept:Angles lying on a straight line always add up to $180^\circ$. This fact is used to form an equation involving $m$.Explanation:Since $PQ$ is a straight line, the angles in the diagram satisfy:$x + y + m + z = 180^\circ$.Group the angles that appear in the given formula:$(x + y + z) + m = 180^\circ$.It is given that $m = \frac{1}{2}(x + y + z)$.Multiply both sides of this equation by 2:$2m = x + y + z$.Now substitute $x + y + z = 2m$ into the straight-line equation:$2m + m = 180^\circ$.Add the terms on the left:$3m = 180^\circ$.Divide both sides by 3:$m = \frac{180^\circ}{3} = 60^\circ$.Answer:$m = 60^\circ$.