Question

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

Explanation:

Step1: Recall isosceles - triangle property

In isosceles triangle $SQT$, since it is isosceles with $ST = QT$, the base - angles are equal. Let $\angle S=\angle Q$. Using the angle - sum property of a triangle ($\angle S+\angle Q+\angle STQ = 180^{\circ}$), and $\angle STQ = 48^{\circ}$, we have $2\angle S=180^{\circ}-\angle STQ$.

Step2: Calculate base - angle measure

$2\angle S=180 - 48=132^{\circ}$, so $\angle S=\frac{132^{\circ}}{2}=66^{\circ}$.

Step3: Consider triangle $STR$

In triangle $STR$, $SR = TR$, so $\angle S=\angle STR$. Since $\angle S = 24^{\circ}$, then $\angle STR = 24^{\circ}$.

Answer:

$24^{\circ}$