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? 90° 60° 120° 150°

Explanation:

Step1: Relate inscribed angle to arc

An inscribed angle is half its intercepted arc.
$\text{arc } WX = 2\times\angle WXZ = 2\times30^\circ = 60^\circ$

Step2: Find semicircle measure

Diameter $XZ$ splits circle into two $180^\circ$ arcs.
$\text{arc } WXYZ = 180^\circ$

Step3: Calculate arc $WUX$

Whole circle is $360^\circ$. Subtract arc $WXZ$.
$\text{arc } WUX = 360^\circ - 180^\circ - 60^\circ = 120^\circ$

Answer:

$120^\circ$