WAEC Mathematics 2016 Paper

Concept:Use the tangent–chord theorem and properties of an isosceles triangle to find the required angle.Explanation:Since $YW$ is a tangent at $X$, the angle between tangent $XW$ and chord $XV$ equals the angle in the alternate segment.Thus, $\angle VUX = \angle VXW = 50^\circ$.In $\triangle UVX$, given $|UV| = |VX|$, the base angles are equal.So, $\angle VXU = \angle VUX = 50^\circ$.Now, $Y$, $X$, and $W$ lie on a straight line.Therefore, $\angle UXY + \angle VXU + \angle VXW = 180^\circ$.Substitute the known values:$\angle UXY + 50^\circ + 50^\circ = 180^\circ$.$\angle UXY + 100^\circ = 180^\circ$.$\angle UXY = 180^\circ - 100^\circ = 80^\circ$.Answer:$\angle UXY = 80^\circ$Option B.