WAEC Mathematics 2015 Paper

Concept:A tangent at a point on a circle is perpendicular to the radius drawn to that point, and in an isosceles triangle the base angles are equal.Explanation:In $\triangle OTN$, $OT = ON$ because both are radii. Therefore, the base angles are equal.Let $x = \angle OTN = \angle TNO$.Using the sum of angles in a triangle:$x + x + 108^\circ = 180^\circ$$2x = 180^\circ - 108^\circ = 72^\circ$$x = \frac{72^\circ}{2} = 36^\circ$So $\angle OTN = 36^\circ$.Since $PTR$ is the tangent at $T$, $OT \perp PT$. Hence $\angle PTO = 90^\circ$.In the diagram, $\angle PTN = \angle PTO + \angle OTN = 90^\circ + 36^\circ = 126^\circ$.Answer:$\angle PTN = 126^\circ$, so the correct option is B. $126^\circ$.