In Fig. 6.10, ∠1 = 60° and ∠6 = 120°. Show that the lines m and n are parallel

Solution:

The figure represents two lines m and n cut by a transversal l

Given, ∠1 = 60° and ∠6 = 120°

We have to show that the lines m and n are parallel.

We know that the vertically opposite angles are equal.

So, ∠1 = ∠3 = 60°

We also know if a transversal cuts two parallel lines then the sum of interior angles lying on the same side of the transversal is supplementary.

The interior angles lying on the same side of the line l are ∠3 and ∠6.

Sum of interior angles = ∠3 + ∠6

Given, ∠6 = 120°

= 60° + 120°

= 180°

Sum of interior angles lying on the same side of the line l is equal to 180°

Therefore, the lines m and n are parallel.

✦ Try This: In the given figure, DE∥BC, ∠ABC=118° and ∠DAB=42°, then ∠ADE is equal to:

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 6

NCERT Exemplar Class 9 Maths Exercise 6.3 Problem 2

In Fig. 6.10, ∠1 = 60° and ∠6 = 120°. Show that the lines m and n are parallel

Summary:

In Fig. 6.10, ∠1 = 60° and ∠6 = 120°. It is shown that the lines m and n are parallel as the sum of interior angles lying on the same side of the line l is equal to 180 degrees

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