Question

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

Explanation:

Step1: Identify equal sides in △SQT

△SQT is isosceles with ST = QT (marked by ticks). So ∠TSQ = ∠TQS.

Step2: Calculate ∠TSQ and ∠TQS

Sum of angles in △SQT: 180° = ∠STQ + ∠TSQ + ∠TQS
180° = 48° + 2∠TSQ → ∠TSQ = (180-48)/2 = 66°

Step3: Identify equal sides in △STR and △QTR

SR = RQ and ST = QT, TR is common. So △STR ≅ △QTR (SSS).

Step4: Find ∠STR

∠STR = ∠QTR, and ∠STR + ∠QTR = ∠STQ = 48°
∠STR = 48°/2 = 24°

Answer:

A. 24°