Lines , , and lie in the same plane. Transversal intersects and , while transversal…

MATHEMATICS · Single correct · CBSE · Mathematics · Lines and Angles · Lines and Angles

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

(c)

m \parallel n

only (d) None of these lines are necessarily parallel