Question

triangle stu is formed by connecting the mid - points 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: Recall the mid - point theorem property

By the mid - point theorem, $ST\parallel RQ$.

Step2: Use the property of corresponding angles

Since $ST\parallel RQ$, $\angle QST$ and $\angle R$ are corresponding angles. Given $\angle R = 54^{\circ}$.

Answer:

$54^{\circ}$