Answer:
C
Step-by-step explanation:
Since PT = QT , then Δ PQT is isosceles with the 2 base angles congruent.
∠ PQT = [tex]\frac{180-36}{2}[/tex] = 72°
∠ TQR = 180° - 72° = 108° ( adjacent angles on a straight line )
Since QT = QR , then Δ QRT is isosceles with 2 base angles congruent
∠ QTR = ∠ QRT = [tex]\frac{180-108}{2}[/tex] = [tex]\frac{72}{2}[/tex] = 36°
∠ TRS = 180° - 36° = 144° ( adjacent angles on a straight line )
Since RT = RS , then Δ TRS is isosceles with 3 bas angle congruent
∠ RTS = ∠ RST = [tex]\frac{180-144}{2}[/tex] = [tex]\frac{36}{2}[/tex] = 18°
Then
∠ PTS = ∠ PTQ + ∠ QTR + ∠ RTS = 36° + 36° + 18° = 90°
