Question

which equation is correct regarding the diagram of circle o? o m∠xzy = 1/2(a + b) o m∠xzy = 1/2(a - b) o m∠xoy = 1/2(a + b) o m∠xoy = 1/2(a - b)

Explanation:

Step1: Recall angle - arc relationship

The measure of an inscribed - angle formed by two chords is half the measure of the intercepted arc. The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc. The measure of an angle formed by two secants, two tangents or a secant and a tangent outside a circle is half the difference of the measures of the intercepted arcs.
For the angle $\angle XZY$ which is formed by a tangent and a chord, if the arc subtended by the angle is $b$ and the other arc is $a$, the measure of $\angle XZY=\frac{1}{2}(a - b)$.
The central - angle $\angle XOY$ is equal to the measure of the arc it subtends. It is not related to the given formula forms in the options for central - angles in this context.

Answer:

$m\angle XZY=\frac{1}{2}(a - b)$ (the second option)