Mathematics

Problem

Lines

\ell

m

, and

n

lie in the same plane. Transversal

p

intersects

\ell

and

m

, while transversal

q

intersects

m

and

n

. A pair of alternate interior angles formed by

p

with lines

\ell

and

m

are equal. A pair of consecutive interior angles formed by

q

with lines

m

and

n

are supplementary. Which statement is necessarily true? a)

\ell \parallel m

only b)

\ell \parallel m

\text{ and }

m \parallel n

m \parallel n

only d) None of these lines are necessarily parallel