WAEC Mathematics 2021 Paper

Concept:Use the alternate segment theorem and the isosceles triangle property of the circle.Explanation:Given $\angle PNQ = 64^\circ$, the angle between the tangent and chord $NQ$.By the alternate segment theorem, the angle in the opposite segment is equal:$\angle NRQ = 64^\circ$.In $\triangle NQR$, since $|\overline{RQ}| = |\overline{RN}|$, the base angles are equal.Let $\angle NQR = \angle QNR = x$.Then, $x + x + 64^\circ = 180^\circ$.So, $2x = 116^\circ$, giving $x = 58^\circ$.The marked angle $t$ is formed by the tangent and chord $NR$.Using the alternate segment theorem again, $t = \angle NQR$.Therefore, $t = 58^\circ$.Answer:$t = 58^\circ$, which is option C.