Questions: VW is tangent to circle U. What is m∠U? m∠U=

Solution Steps

A radius drawn to the point of tangency is perpendicular to the tangent line. Therefore, $\overline{UV}$ is perpendicular to $\overline{VW}$. This makes $\angle UVW$ a right angle, meaning its measure is $90^\circ$.

Triangle $UVW$ has angles $\angle U$, $\angle V$, and $\angle W$. The sum of the angles in any triangle is $180^\circ$. We know that $m\angle V = 90^\circ$ and $m\angle W = 38^\circ$. Therefore, \begin{align_} \label{eq:triangle} m\angle U + m\angle V + m\angle W &= 180^\circ \\ m\angle U + 90^\circ + 38^\circ &= 180^\circ \\ m\angle U + 128^\circ &= 180^\circ \\ m\angle U &= 180^\circ - 128^\circ \\ m\angle U &= 52^\circ\end{align_}

Final Answer