Question

In the diagram below, line MN is a diameter of the circle. Find angle XYZ, in degrees.

[asy]
unitsize(2 cm);

pair A, B, C, E, F, O;

O = (0,0);
E = dir(180);
F = dir(0);
A = dir(140);
C = dir(60);
B = extension(A,F,C,E);

draw(Circle((0,0),1));
draw(E--C--O--A--F--cycle);

label("$X$", A, NW);
dot("$Y$", B, N);
label("$Z$", C, NE);
label("$M$", E, W);
label("$N$", F, dir(0));
dot("$O$", O, S);
label("$80^\circ$", dir(30), NE);
label("$35^\circ$", dir(160), W);
[/asy]

Answer 1

By chasing the angles, angle XYZ works out to 133.5 degrees.