Question

triangle stu is formed by connecting the midpoints of the side of triangle pqr. the measures of the interior angles of triangle pqr are shown. find the measure of ∠qst. figures not necessarily drawn to scale.

Explanation:

Step1: Use the mid - segment theorem

Since \(STU\) is formed by connecting the mid - points of \(\triangle PQR\), \(ST\parallel PR\) (by the mid - segment theorem: the line segment connecting the mid - points of two sides of a triangle is parallel to the third side).

Step2: Use the property of parallel lines and transversal

When \(ST\parallel PR\) and \(PQ\) is a transversal, \(\angle QST\) and \(\angle P\) are corresponding angles.
Given \(\angle P = 44^{\circ}\) (from the measures of the interior angles of \(\triangle PQR\))

Answer:

\(44^{\circ}\)