JAMB Mathematics 2016 Paper

Concept:Use the angle-sum rule of a triangle and the equal-angle property of a cyclic quadrilateral.Explanation:The two marked angles $80^\circ$ and $20^\circ$ are part of the triangle whose third angle is $\angle TVS$.So the sum of the angles in that triangle gives:$$\angle TVS = 180^\circ - (80^\circ + 20^\circ)$$$$\angle TVS = 180^\circ - 100^\circ = 80^\circ$$In a cyclic quadrilateral, angles that subtend the same chord are equal.The required angle $\angle TSV$ stands on the same chord as $\angle TVS$.Therefore:$$\angle TSV = \angle TVS = 80^\circ$$Answer:$\angle TSV = 80^\circ$Correct option: B. $80^\circ$