Question

in the diagram below,PQ is parallel to OL.Is OL parallel to ST? give reasons.

Answer 1

Yes, because theydo not intersect each other at any point so ST || OL

Answer 2

Given:

PQ║OL

To prove:

OL║ST

Solution:

In the figure attached,

PQ║OL and QM is a transverse,

m∠PQM + m∠QMS = 180° [Interior consecutive angles]

110° + m∠QMS = 180°

m∠QMS = 70°

Now m∠QMO + m∠QMS + m∠SML = 180°

70 + 60 + m∠SML = 180

m∠SML = 50°

If OL║ST and SM is a transverse,

Then sum of consecutive interior angles will be 180°.

m∠TSM + m∠SML = 180°

By substituting the values of the angles,

130° + 50° = 180°

180° = 180° [True]

Therefore, OL║ST is true.