Question

find the measure of \\( \angle u w v \\).

Explanation:

Step1: Use the property of alternate interior angles

Since \( SR\parallel UT\), \( \angle SVW=\angle UWW\) (alternate interior angles). Also, \( \angle SVW=(7x + 10)^{\circ}\) and \( \angle UWW=(6x - 12)^{\circ}\). So, \( 7x+10 = 6x - 12\).

$$\begin{align*} 7x+10&=6x - 12\\ 7x-6x&=-12 - 10\\ x&=-22 \end{align*}$$

Step2: Calculate the measure of \( \angle UWW\)

Substitute \( x = 22\) into \( \angle UWW=(6x - 12)^{\circ}\).

$$\begin{align*} \angle UWW&=6\times22-12\\ &=132 - 12\\ &=120^{\circ} \end{align*}$$

Answer:

\(120\)