WAEC Mathematics 2021 Paper

Concept:The triangle is isosceles because $|XY| = |ZY|$, so the base angles $\angle X$ and $\angle Z$ are equal.Also, when a side of a triangle is produced, the exterior angle equals the sum of the two opposite interior angles.Explanation:Here, $YZ$ is produced to $T$, so $\angle XYT$ is the same as the interior angle $\angle XYZ$.Therefore, $\angle XYZ = 40^\circ$.Let $\angle X = \angle Z = x$.Using the angle sum of triangle $XYZ$:$x + x + 40^\circ = 180^\circ$$2x = 140^\circ$$x = 70^\circ$So, $\angle X = 70^\circ$ and $\angle Z = 70^\circ$.Now, $\angle XZT$ is the exterior angle at $Z$.$\angle XZT = \angle X + \angle Y = 70^\circ + 40^\circ = 110^\circ$Answer:$\angle XZT = 110^\circ$, which is option A.