Question: Line segment $SU$ is a diameter of circle $V$. What is the measure of arc $ST$? 56° 68° 112° 163° A circle diagram is shown at the top-left. The circle has center $V$, with points $T$ at the upper-left, $U$ at the upper-right, and $S$ at the lower-left. Line segments $ST$ and $TU$ are chords, and $SU$ is a diameter passing through $V$. The angle at $V$ between $VS$ and $VT$ is labeled 34°. Position hint: top-left.

1. **Problem Statement:** We are given a circle with center $V$ and diameter $SU$. Points $S$, $T$, and $U$ lie on the circle. The angle $\\angle SVT$ at the center $V$ is $34^\circ$. We need to find the measure of the arc $ST$. 2. **Key Concept:** The measure of a central angle in a circle is equal to the measure of the arc it intercepts. Here, the central angle $\angle SVT$ intercepts the arc $ST$. 3. **Given:** - $SU$ is a diameter, so $V$ is the center. - $\angle SVT = 34^\circ$ 4. **Find:** Measure of arc $ST$. 5. **Solution:** - Since $\angle SVT$ is a central angle, the measure of arc $ST$ is equal to $34^\circ$. 6. **Check the options:** - $56^\circ$, $68^\circ$, $112^\circ$, $163^\circ$ 7. The angle given is $34^\circ$, but none of the options match $34^\circ$. We need to consider the arc $ST$ which is the major arc or minor arc. 8. Since $SU$ is a diameter, the circle is divided into two semicircles of $180^\circ$ each. 9. The central angle $\angle SVT = 34^\circ$ corresponds to the minor arc $ST$. 10. The measure of the major arc $ST$ would be $360^\circ - 34^\circ = 326^\circ$, which is not an option. 11. However, the problem likely refers to the arc $ST$ intercepted by the chord $ST$, which is twice the inscribed angle subtending the same arc. 12. The inscribed angle $\angle SVT$ is $34^\circ$, so the arc $ST$ measure is $2 \times 34^\circ = 68^\circ$. 13. **Final answer:** $\boxed{68^\circ}$