1. **State the problem:** We need to find the measure of the major arc $m\widehat{VXW}$ in a circle centered at $U$ with points $V$, $X$, and $W$ on the circle. $V$ and $W$ lie on a secant line through $U$, and $V$ is a tangent point. 2. **Recall relevant properties:** - A tangent to a circle is perpendicular to the radius at the point of tangency. - The measure of an arc intercepted by an angle formed by a tangent and a secant can be found using the tangent-secant angle theorem. 3. **Identify the angle and arcs:** - The angle formed at $V$ by the tangent and the secant $VW$ intercepts the arc $m\widehat{VXW}$. 4. **Use the tangent-secant angle theorem:** - The measure of the angle formed by a tangent and a secant is half the measure of the intercepted arc. - Let $\angle V$ be the angle between the tangent at $V$ and the secant $VW$. 5. **Express the arc measure:** $$m\angle V = \frac{1}{2} m\widehat{VXW}$$ 6. **Find $m\angle V$:** - Since $V$ is a tangent point, $\angle V$ is the angle between the tangent and the secant. - If $\angle V$ is known or can be measured, then: $$m\widehat{VXW} = 2 m\angle V$$ 7. **Conclusion:** - Without specific angle measures or lengths, the measure of the major arc $m\widehat{VXW}$ is twice the angle formed at $V$ by the tangent and secant. **Final answer:** $$m\widehat{VXW} = 2 m\angle V$$