triangle stu is formed by connecting the midpoints of the side of triangle pqr. the measures of the interior…

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.

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.

Answer

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})