Question

in the given figure AC parallel to GD and ae parallel to bf find the values of X Y and Z

Answer 1

As AC || BD,
115°+x=180° (Interior Angle)
Therefore x=65°.

x+y+86=180(Supplementary angle)
y+65+85=180
y+150=180
y=30°

As AE || BF,
z+y=180(Interior Angle)
z+30=180
z=150°

Answer 2

since A.C. is parralel to BD and AN is a transversal we have
angle cab + angle dba = 180 ( co interior angles are supplementary theroem)
therefore
115+x=180
x=180-115=65

now we have dbg is a straight line therefore
x+y+angle fbg = 180 (linear pair)
65+y+85=180
y+150=180
y=30

since ae is parralel to bg and ab is a transversal
therefore
z+y=180(cointerior angles are supplementary)
z+30=180
z=150