Given: AB and CD are two parallel lines and EF is a transversal which intersect them at M and N respectively forming two pairs of interior angles ∠1, ∠3 and ∠2, ∠4.
To Prove: (i) ∠1 + ∠3 = 180°
or ∠2 + ∠4 = 180°
Proof: Since ray ND stands on line EF,
∠3 + ∠5 = 180° …(i) (linear pair of angles)
But ∠1 = ∠5 …(ii) (Corresponding angles as AB || CD)
From (i) and (ii), we get
∠1 + ∠3 = 180° …(iii)
Again ray CN stands on EF,
∠2 + ∠6 = 180° (Linear pair of angles)
But ∠4 = ∠6 (Corresponding angles as AB || CD)
⇒ ∠2 + ∠4 = 180° …(iv)
Hence, we can say if a transversal intersects two parallel lines, then each pair of interior angles are supplementary
i.e. ∠1 + ∠3 = 180°
or ∠2 + ∠4 = 180°
