Answer
x=113$^{\circ}$
y=67$^{\circ}$
z=36$^{\circ}$
Work Step by Step
m$\angle$DEA=180-36-77
m$\angle$DEA=67$^{\circ}$
Angles x and DEA form a straight line so they are supplementary.
m$\angle$x=180-67
m$\angle$x=113$^{\circ}$
Angles y and DEA are corresponding angles so they are congruent.
m$\angle$y=m$\angle$DEA
m$\angle$y=67$^{\circ}$
Angles D and ECB are alternate interior angles so they are supplementary.
m$\angle$ECB=180-m$\angle$D
m$\angle$ECB=180-77
m$\angle$ECB=103$^{\circ}$
m$\angle$z=m$\angle$ECB-m$\angle$y
m$\angle$z=103-67
m$\angle$z=36$^{\circ}$
