Question

triangles
triangle sqt is isosceles. the measure of angle stq is 48. what is the measure of ∠str?
38
48
76
24

Explanation:

Step1: Use the property of isosceles triangles

Since triangle \(SQT\) is isosceles (\(ST = QT\)), and \(R\) is the mid - point of \(SQ\) (as \(SR=RQ\)), then \(TR\) is the angle bisector of \(\angle STQ\).

Step2: Calculate \(\angle STR\)

We know that \(\angle STQ = 48^{\circ}\). By the angle - bisector property, \(\angle STR=\frac{1}{2}\angle STQ\).
So, \(\angle STR=\frac{1}{2}\times48^{\circ}\)
\( = 24^{\circ}\)

Answer:

\(24^{\circ}\)