Question

YZ is tangent to the circle at Z. Find the measure of minor arc WX
.

Answer 1

Explanation:

the angle at Y = 1/2 × (arc angle WZ - arc angle ZX).

so,

42 = (arc angle WZ - 51)/2

84 = arc angle WZ - 51

135° = arc angle WZ

the arc angle WX is the remainder of the whole circle to the sum of the arc angles WZ and ZX :

arc angle WX = 360 - 135 - 51 = 174°