Question

in the figure below, $\triangle rst$ is drawn. the line $overleftrightarrow{urv}$ is drawn such that $overleftrightarrow{urv} parallel overline{st}$.$mangle rst = mangle sru$ because they are alternate interior angles.$mangle str =$ $quad$ because they are

Explanation:

First, use the property of parallel lines: when a transversal cuts two parallel lines, alternate interior angles are congruent. For $\angle STR$, the transversal is $\overline{TR}$ cutting parallel lines $\overleftrightarrow{URV}$ and $\overline{ST}$. The angle corresponding to $\angle STR$ is $\angle URT$ (which is $x^\circ$). Then, we can use the triangle angle sum theorem to find $x$ first: the sum of angles in $\triangle RST$ is $180^\circ$. Calculate $\angle SRT = 180^\circ - 50^\circ - 72^\circ = 58^\circ$. Since $\angle SRU = \angle RST = 50^\circ$ (alternate interior angles), then $x = 180^\circ - 50^\circ - 58^\circ = 72^\circ$, which matches $\angle STR$. So $\angle STR$ is congruent to $\angle URT$ (or $x^\circ$) because they are alternate interior angles.

Answer:

$m\angle STR = m\angle URT$ (or $x^\circ$) because they are alternate interior angles.