Given, the measure of arc VXY= 320 degrees.
Since the sum of the major and minor arcs of a circle is 360 degrees, we can write
[tex]\begin{gathered} m(\text{arc VY)+}m(arc\text{ VXY})\text{=}360^{\circ} \\ m(\text{arc VY)=}360^{\circ}-m(arc\text{ VXY}) \\ \text{=}360^{\circ}-320^{\circ} \\ =^{}40^{\circ} \end{gathered}[/tex]
If an angle is inscribed in a circle, then the angle equals one half the measure of its intercepted arc.
Arc VY is the intercepted arc of
Hence, [tex]\begin{gathered} <\text{VXY}=\frac{1}{2}m(\text{arc VY)} \\ =\frac{1}{2}\times40^{\circ} \\ =20^{\circ} \end{gathered}[/tex]Therefore, the measure of angle VXY is 20 degrees.
