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In the given figure, find out which pair of lines are parallel

Solution:

Given, the figure represents the lines AB and CD cut by the lines EF, GH and KP.

∠1= 123°

∠2 = 57°

∠3 = 55°

∠5 = 122°

We have to find the pair of parallel lines.

From the properties of angles formed by transversal on two parallel lines,

If two parallel lines are intersected by a transversal,

(i) each pair of corresponding angles is equal.

(ii) each pair of alternate interior angles is equal.

(iii) each pair of interior angles on the same side of the transversal is supplementary.

Considering the lines EF and GH cut by transversal CD

∠1 and ∠2 are the interior angles on the same side of the transversal.

So, ∠1 + ∠2 = 123° + 57°

= 180°

Therefore, EF is parallel to GH

Considering the lines GH and KP cut by transversal CD

∠2 and ∠3 are the corresponding angles.

57° ≠ 55°

Therefore, GH and KP are not parallel.

Considering the lines EF and KP cut by transversal CD

∠1 and ∠3 are the interior angles on the same side of the transversal.

So, ∠1 + ∠3 = 123° + 55°

= 178°

The sum of interior angles is not equal to 180°

Therefore, EF is not parallel to KP.

Considering lines AB and CD cut by transversal GH,

The vertically opposite angles are ∠2 and ∠4.

∠2 = ∠4 = 57°

∠4 and ∠5 are the interior angles on the same side of the transversal.

So, ∠4 + ∠5 = 122° + 57°

= 179°

The sum of interior angles is not equal to 180°

Therefore, AB is not parallel to CD

✦ Try This: OA and OB are opposite rays. If x = 75°, what is the value of y?

OA and OB are opposite rays. If x = 75°, what is the value of y

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 5

NCERT Exemplar Class 7 Maths Chapter 5 Sample Problem 18

Summary:

EF and GH represent a pair of parallel lines.

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