Geometry Practice Test 4

∠VTR = 52°
∠VTR = x° (Alternative interior segment property)
∠x = 52°
PRST is a concyclic quadrilateral.
∠x + ∠z = 180°
52° + ∠z = 180°
∠z = 180° - 52
∠z = 128°

In ΔPTR,
PT = TR
⇒∠x = ∠1
⇒∠PTU = ∠1 = 52° (Alternative interior segment property)
∠QTU = 90°
∠QTU -∠PTU = y
y = 90° - 52°
y = 38°
∠x + ∠y + ∠z = 52° + 38° + 128° = 218°