WAEC Mathematics 2017 Theory — Question 17

Model answer

Construction: Join V to W. Since ΔVZY is isosceles (|VZ|=|YZ|), base angles ∠ZVY=∠ZYV=52°. ∠XVZ+∠ZVY=180° (angles on a straight line), so ∠XVZ=128°. In ΔXVZ: ∠VXZ+∠XVZ+∠VZX=180° → 20+128+∠VZX=180 → ∠VZX=32°. Since ∠VZX and ∠VYX are angles in the same segment on the same chord VX, ∠VYX=∠VZX=32°. Finally, ∠VYW+∠WYZ=∠ZYV → combining with the established angles, ∠WYZ=52°-32°=20°.