1. **State the problem:** We are given a circle with points S, T, U, V on the circumference and center O. The measure of arc SV is 120° and the inscribed angle at T is 82°. We need to find the measure of arc VU. 2. **Recall the inscribed angle theorem:** An inscribed angle measures half the measure of its intercepted arc. That is, if an inscribed angle intercepts an arc, then $$\text{angle} = \frac{1}{2} \times \text{arc measure}$$ 3. **Identify the intercepted arc for angle T:** The inscribed angle at T intercepts the arc SVU (the arc from S to U passing through V). 4. **Calculate the measure of arc SVU:** Since angle T = 82°, then $$82 = \frac{1}{2} \times \text{arc SVU}$$ Multiply both sides by 2: $$2 \times 82 = \cancel{2} \times \frac{1}{\cancel{2}} \times \text{arc SVU}$$ $$164 = \text{arc SVU}$$ 5. **Use the total circle measure:** The total measure of the circle is 360°. The arc SVU consists of arcs SV and VU, so $$\text{arc SVU} = \text{arc SV} + \text{arc VU}$$ Substitute known values: $$164 = 120 + \text{arc VU}$$ 6. **Solve for arc VU:** $$\text{arc VU} = 164 - 120 = 44$$ **Final answer:** The measure of arc VU is $44^\circ$.