Question

the quadrilateral below is divided into two triangles by $overline{tu}$, with $overline{rt}congoverline{st}$. which of the following is a possible measure for $angle{stu}$?

Explanation:

Step1: Recall triangle - angle properties

In a triangle, the sum of interior angles is 180°. Also, in \(\triangle RTU\), we know one angle is 42°. Let \(\angle RTU = 42^{\circ}\). In \(\triangle STU\) and \(\triangle RTU\), since \(RT\cong ST\) and they share side \(TU\).

Step2: Analyze angle - size relationships

The measure of \(\angle STU\) must be greater than 0°. Also, considering the geometric constraints of the two - triangle formation, we know that \(\angle STU\) cannot be equal to 42° (otherwise, the figure would have some special congruence conditions that are not indicated to be the case here). Among the given options, 45° is a possible measure for \(\angle STU\) as it satisfies the general geometric rules for angles in a triangle formed by the given quadrilateral division.

Answer:

45°