in circle v, angle wxz measures 30°. line segments wv, xv, zv, and yv are radii of circle v. what is the…

Explanation:

Step1: Recall the inscribed - angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc. Angle $WXZ$ is an inscribed angle and it intercepts arc $WZ$. Given $\angle WXZ = 30^{\circ}$, then the measure of arc $WZ$ is $m\overset{\frown}{WZ}=2\times\angle WXZ$. $m\overset{\frown}{WZ}=2\times30^{\circ}=60^{\circ}$

Step2: Find the measure of arc $WUX$

The sum of the measures of the arcs of a circle is $360^{\circ}$. Arc $WUX$ and arc $WZ$ are such that $m\overset{\frown}{WUX}+m\overset{\frown}{WZ}=360^{\circ}$. Also, since the circle is symmetric and we assume that we are looking for the non - minor arc $WUX$, and the central angle corresponding to arc $WUX$ and arc $WZ$ together make a full - circle. Another way is to note that the central angle of the whole circle is $360^{\circ}$. If we consider the relationship between the inscribed angle and the arc, and assume we want the larger arc between the two arcs formed by points $W$ and $X$. The measure of arc $WUX = 360^{\circ}- 240^{\circ}=120^{\circ}$ (because the minor arc corresponding to the inscribed - angle relationship has a central - angle measure of $60^{\circ}$, and the non - minor arc $WUX$ has a central - angle measure of $360 - 60=120^{\circ}$). In terms of the inscribed angle, the non - minor arc $WUX$ is the arc that is not the one directly related to the given inscribed angle in the simple half - relationship. The measure of arc $WUX$ is $120^{\circ}$ as the central angle corresponding to it is $120^{\circ}$ (a full circle is $360^{\circ}$ and the other arc related to the given inscribed angle has a central - angle measure of $60^{\circ}$).

Answer:

$120^{\circ}$