Question

in circle v, angle wxz measures 30°. line segments wv, xv, zv, and yv are radii of circle v. what is the measure of arc wux in circle v? 60° 120° 90° 150°

Explanation:

Step1: Recall inscribed - angle theorem

The measure of an inscribed angle is half the measure of the intercepted arc.

Step2: Identify the inscribed angle and intercepted arc

The inscribed angle $\angle{WXZ}=30^{\circ}$, and the arc it intercepts is $\overset{\frown}{WZ}$. So the measure of $\overset{\frown}{WZ}=2\times\angle{WXZ}=60^{\circ}$.

Step3: Find the measure of $\overset{\frown}{WUX}$

The measure of a full - circle is $360^{\circ}$. The arc $\overset{\frown}{WUX}$ and $\overset{\frown}{WZ}$ are related such that $\overset{\frown}{WUX}=360^{\circ}-\overset{\frown}{WZ}$. Since $\overset{\frown}{WZ} = 60^{\circ}$, then $\overset{\frown}{WUX}=360^{\circ}- 60^{\circ}=300^{\circ}$. But if we assume you want the minor arc $\overset{\frown}{WUX}$, we note that the central angle corresponding to $\overset{\frown}{WUX}$ is $120^{\circ}$ (because the central angle is twice the inscribed angle subtended by the same arc and the other part of the circle related to the inscribed - angle setup). The measure of the minor arc $\overset{\frown}{WUX}$ is $120^{\circ}$ as the central angle of the arc $\overset{\frown}{WUX}$ (the angle at the center $V$ subtended by $\overset{\frown}{WUX}$) is $120^{\circ}$.

Answer:

$120^{\circ}$