Question

What is the measure of minor arc XZ , given that YX and YZ are tangent to center point O?

Answer 1

There is a simple solution to this.
Major arc XZ = 220°
Since all circles = 360° then
Minor arc XZ = 140°

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Perhaps they want you to use the method in the attachment.
angle y = 1/2 (Major Arc XZ - Minor Arc XZ)
angle y = .5 * Major Arc XZ -.5 * Minor Arc XZ
.5 * Minor Arc XZ = .5 * Major Arc XZ - angle y
.5 * Minor Arc XZ = (.5 * 220) -40
.5 * Minor Arc XZ = 110 -40
.5 * Minor Arc XZ = 70
Minor Arc XZ = 140