Fletcher Glover

Mathematics

24 November, 07:59

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]