Answer:
[tex]m\widehat{VU}=120^{\circ}[/tex]
Step-by-step explanation:
The angle [tex]\angle TUV[/tex] forms arc [tex]\widehat{TV}[/tex]. The measure of this arc is twice the measure of angle [tex]\angle TUV[/tex], since [tex]U[/tex] is a point on the circle. Since [tex]\overline{TU}[/tex] forms an arc [tex]\widehat{TU}[/tex], we can set up the following equation:
[tex]\widehat{TV}+\widehat{VU}=\widehat{TU}[/tex].
Since arc TU represents half of a circle and there are 360 degrees in a circle, we can substitute the following values and solve for the measure of arc VU:
[tex]\\2\cdot 30^{\circ}+\widehat{VU}=180^{\circ},\\60^{\circ}+\widehat{VU}=180^{\circ},\\m\widehat{VU}=\boxed{120^{\circ}}[/tex]
