Answer:
D
Explanation:
Since Δ QTS is isosceles then the base angles are congruent , that is
∠ TQS = ∠ QST = y
∠ QST and ∠ RST are a linear pair and sum to 180° , that is
∠ QST + ∠ RST = 180
y + ∠ RST = 180 ( subtract y from both sides )
∠ RST = 180 - y
the sum of the 3 angles in Δ TRS = 180° , that is
∠ RTS + ∠ TRS + ∠ RST = 180
∠ RTS + x + 180 - y = 180 ( subtract 180 from both sides )
∠ RTS + x - y = 0 ( subtract x - y from both sides )
∠ RTS = y - x