In the figure above , Ts//xy and XY = TY, ∠SYZ = 34∘ ∘ , ∠TXY = 47∘ ∘ , find the angle marked n

In the figure above , Ts//xy and XY = TY, ∠SYZ = 34${}^{\circ }$, ∠TXY = 47${}^{\circ }$, find the angle marked n

Answer Details

In Δ TYX
XY = TY ∴y =47${}^{\circ }$ base ∠s of ISCΔ
But y+x+34+47 = 180 interior
opposite ∠s are supplementary
47 + x + 34 + 47 = 180
x + 128= 180
x = 180- 128
x = 52${}^{\circ }$