Question

Can somebody help me with the geometry equation.

Answer 1

`m\widehat{VU}=120^(\circ)`

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)}`