JAMB Mathematics 2023 Paper

Concept:Use the tangent properties and the alternate segment theorem to find the required angle.Explanation:In $\triangle PSR$, $PS = SR$ because both are tangents drawn from the same external point $R$.Therefore, $\triangle PSR$ is isosceles, so $\angle SRP = \angle SPR$.Using the sum of angles in a triangle:$\angle PSR + \angle SRP + \angle SPR = 180^\circ$.Substitute the equal angles:$\angle PSR + 2\angle SRP = 180^\circ$.Given $\angle PSR = 36^\circ$, we get:$36^\circ + 2\angle SRP = 180^\circ$.So $2\angle SRP = 144^\circ$, which gives $\angle SRP = 72^\circ$.By the alternate segment theorem, the angle between tangent $SR$ and chord $SP$ equals the angle in the alternate segment:$\angle SRP = \angle PQR$.Thus, $\angle PQR = 72^\circ$.Answer:A. $72^\circ$