In Fig. 8.138, if lines l and m are parallel, then x =

l ‖ m

Let transversal be n and ∠1 = 65^o

∠2 = 20^o

∠3 = x

Since,

l ‖ m and n cuts them so,

∠1 + ∠4 = 180^o (Co. interior angle)

65^o + ∠4 = 180^o

∠4 = 115^o (i)

∠4 = ∠5 = 115^o (Vertically opposite angle)

∠2 + ∠5 + ∠3 = 180^o

20^o + 115⁰ + x = 180^o

x = 45^o