BECE Mathematics 2013 Paper

Concept:The construction shows the bisection of a $60^\circ$ angle, which produces a $30^\circ$ angle at point $P$.Explanation:From point $P$, the given figure shows a $60^\circ$ angle formed by two rays.An arc is drawn with centre $P$, cutting both rays at equal distances from $P$.Keeping the same compass width, two more arcs are drawn from those two cutting points.These arcs intersect at a point inside the angle.A straight line is then drawn from $P$ to that intersection point.This line is the angle bisector.It divides the $60^\circ$ angle into two equal parts.So the angle between the original ray and the bisector is $60^\circ \div 2 = 30^\circ$.Thus, the construction is specifically creating an angle of $30^\circ$ at $P$.Answer:C. Constructing an angle of $30^\circ$ at $P$.