Given:
On circle O, the measure of arc SV is 120° and m∠STU = 82°
We need to determine the measure of arc VU
Measure of arc VU:
The measure of arc VU can be determined using the inscribed angle theorem.
Thus, we have;
[tex]m \angle STU=\frac{1}{2} m (\widehat{SU})[/tex]
The measure of SU is SU = SV + VU
Using this in the above formula, we get;
[tex]m \angle STU=\frac{1}{2} (m \widehat{SV}+m \widehat{VU})[/tex]
Substituting m∠STU = 82° and [tex]m \widehat{S V}=120^{\circ}[/tex], we have;
[tex]82^{\circ}=\frac{1}{2}(120^{\circ}+m \widehat{VU})[/tex]
[tex]164^{\circ}=120^{\circ}+m \widehat{VU}[/tex]
[tex]44^{\circ}=m \widehat{VU}[/tex]
Hence, the measure of arc VU is 44°
