In Fig., AB || CD and AC || BD. Find the values of x, y, z.
(i) Since AC || BD and CD || AB, ABCD is a parallelogram.
∠CAB + ∠ACD = 180° (Sum of adjacent angles of a parallelogram)
∴ ∠ACD = 180° − 65° = 115°
∠CAD = ∠CDB = 65° (Opposite angles of a parallelogram)
∠ACD = ∠DBA = 115° (Opposite angles of a parallelogram)
AC || BD and CD || AB
∠DAC = x = 40° (Alternate interior angle)
∠DAB = y = 35° (Alternate interior angle)
In Fig., state which lines are parallel and why?
Since ∠ACD and ∠CDE are alternate and equal angles, so
∠ACD = 100° = ∠CDE
∴ AC || EF
In Fig. 87, the corresponding arms of ∠ABC and ∠DEF are parallel. If ∠ABC = 75°, find ∠DEF.
Construction : Let G be the point of intersection of lines BC and DE.
∵ AB || DE and BC || EF
∴ ∠ABC=∠DGC=∠DEF=75°∠ABC=∠DGC=∠DEF=75° (Corresponding angles)