In the diagram below, $\overline{AB}$ and $\overline{EF}$ are parallel. If $\angle ABC = 129^\circ$, $\angle BCD = 180^\circ$, and $\angle ECD = 56^\circ$, then what is $\angle CEF$, in degrees?

Question

In the diagram below, $\overline{AB}$ and $\overline{EF}$ are parallel. If $\angle ABC = 129^\circ$, $\angle BCD = 180^\circ$, and $\angle ECD = 56^\circ$, then what is $\angle CEF$, in degrees?

[asy]
unitsize(2.5 cm);

pair P, Q, R, SS, T, U;
P = (1,0);
Q = (0,0);
R = (-0.3,-0.6);
SS = 2.5*R;
T = R + (0.4,-0.5);
U = T + (1,0);

dot(P,p=black+3bp);
dot(SS,p=black+3bp);
dot(U,p=black+3bp);

draw(U--T--R--Q--P);
draw(R--SS);
label("$A$",P,E);
label("$F$",U,E);
label("$B$",Q,N);
label("$E$",T,S);
label("$C$",R,NW);
label("$D$",SS,S);
[/asy]

Answer 1

In the diagram below, $\overline{AB}$ and $\overline{EF}$ are parallel. If $\angle ABC = 129^\circ$, $\angle BCD = 180^\circ$, and $\angle ECD = 56^\circ$, then what is $\angle CEF$, in degrees?

Since $\overline{AB} \parallel \overline{EF}$, we have $\angle ABC = \angle CEF$. Therefore, $\angle CEF = \boxed{129^\circ}$.