Question

in the figure below, $\triangle stu$ is drawn. the line $overleftrightarrow{vsw}$ is drawn such that $overleftrightarrow{vsw}paralleloverline{tu}.$
$mangle stu =$ because they are

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In \(\triangle STU\), we know two of the angles: \(\angle T = 38^{\circ}\) and \(\angle U=61^{\circ}\). Let \(\angle S = y\). Then \(y + 38^{\circ}+61^{\circ}=180^{\circ}\).

Step2: Solve for \(\angle S\) in \(\triangle STU\)

\[

$$\begin{align*} y&=180^{\circ}-(38^{\circ} + 61^{\circ})\\ y&=180^{\circ}-99^{\circ}\\ y& = 81^{\circ} \end{align*}$$

\]

Step3: Use linear - pair property

Since \(\angle x\) and \(\angle S\) in \(\triangle STU\) form a linear - pair (a straight - line measures 180°), if \(\angle S = 81^{\circ}\), then \(x+81^{\circ}=180^{\circ}\).

Step4: Solve for \(x\)

\[

$$\begin{align*} x&=180^{\circ}-81^{\circ}\\ x&=99^{\circ} \end{align*}$$

\]

Answer:

99