Answer:
To prove that sum of the measures of triangle XYZ is 180°
Out of the four options given
A. Construct a bisector of angle Z
B. Construct a midpoint of segment YZ
C. Construct a line parallel to segment XZ
D. Construct a perpendicular bisector of segment XY
Option C Construct a line parallel to segment XZ is correct.
Draw a line l passing through vertex Y parallel to XZ. As alternate angles becomes equal, and applying linear pair axiom on point Y and then By substitution you can prove sum of the measures of angles of triangle XYZ is 180°.
