Question

On circle o below the measure of sv is 120 degrees. what is the measure of vu?

Answer 1

To determine the measure of arc VU, given that we know the measure of ∠STU and arc SV, the first step is to determine the measure of arc SVU.

The relationship between the measure of an angle that has a vertex on the circle and its intercepted arc is that the measure of the said arc is twice the measure of the angle. Then the measure of arc SVU is twice the measure of ∠STU

`\begin{gathered} \text{arcSVU}=2\angle STU \\ \text{arcSVU}=2\cdot82 \\ \text{arcSVU}=164º \end{gathered}`

Now, arc SVU is formed by arcs SV and VU, so to determine the measure of VU you have to subtract SV from SVU:

`\begin{gathered} \text{SVU}=SV+VU \\ VU=\text{SVU-SV} \\ VU=164-120 \\ VU=44º \end{gathered}`

Arc VU measures 44º