Question

If a transversal intersects two parallel lines then each pair of consecutive interior angle is _________.

Answer 1

AB and CD are two parallel lines intersected by a transversal PQ at R and S, respectively. Here, the pair of consecutive interior angles are ∠BRS and ∠DSR & ∠ARS and ∠CSR.

Now,

∠PRB + ∠BRS = 180º .....(1) (Linear pair)

∠PRB = ∠DSR .....(2) (Corresponding angles)

From (1) and (2), we have

∠DSR + ∠BRS = 180º

Similarly, ∠ARS + ∠CSR = 180º

Thus, if a transversal intersects two parallel lines, then each pair of consecutive interior angles are supplementary.

If a transversal intersects two parallel lines then each pair of consecutive interior angle is __supplementary__.