Question

Can somebody help me with the geometry equation.

Answer 1

Answer:

$m\widehat{VU}=120^{\circ}$

Step-by-step explanation:

The angle $\angle TUV$ forms arc $\widehat{TV}$. The measure of this arc is twice the measure of angle $\angle TUV$, since $U$ is a point on the circle. Since $\overline{TU}$ forms an arc $\widehat{TU}$, we can set up the following equation:

$\widehat{TV}+\widehat{VU}=\widehat{TU}$.

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:

$\\2\cdot 30^{\circ}+\widehat{VU}=180^{\circ},\\60^{\circ}+\widehat{VU}=180^{\circ},\\m\widehat{VU}=\boxed{120^{\circ}}$