We are given a quadrilateral TUVW inscribed in a circle. The measure of angle V is given as $101^{\circ}$. We need to find the measure of arc UW.

1. Problem Description

We are given a quadrilateral TUVW inscribed in a circle. The measure of angle V is given as $101^{\circ}$. We need to find the measure of arc UW.

2. Solution Steps

Since quadrilateral TUVW is inscribed in a circle, opposite angles are supplementary. Therefore, the sum of angle T and angle V is $180^{\circ}$.

We have $angle V = 101^{\circ}$. Therefore, $angle T + 101^{\circ} = 180^{\circ}$.

Subtracting $101^{\circ}$ from both sides gives $angle T = 180^{\circ} - 101^{\circ} = 79^{\circ}$.

The measure of an inscribed angle is half the measure of its intercepted arc.

$angle T = \frac{1}{2} m\stackrel{\frown}{UW}$

Thus, $m\stackrel{\frown}{UW} = 2 * angle T = 2 * 79^{\circ} = 158^{\circ}$.

3. Final Answer

158