# In Fig. 6.10, ∠1 = 60° and ∠6 = 120°. Show that the lines m and n are parallel. It is given to us –

1 = 60°

6 = 120°

We have to show that m and n are parallel to each other.

We can see that l is a ray standing on the line m. So, by linear pair axiom,

1 + 4 = 180°

60° + 4 = 180°

4 = 180° - 60°

4 = 120° - - - - (i)

Similarly,

1 + 2 = 180°

60° + 2 = 180°

2 = 180° - 60°

2 = 120° - - - - (ii)

Again, 2 + 3 = 180°

120° + 3 = 180°

3 = 180° - 120°

3 = 60° - - - - (iii)

Since, 6 = 120° and 2 = 120° [from equation (ii)],

We can say that these corresponding angles are equal, i.e.,

6 = 2 = 120° - - - - (iv)

We can say that l is a ray standing on the line n. By linear pair axiom,

6 + 5 = 180°

120° + 5 = 180°

5 = 180° - 120°

5 = 60° - - - - (v)

Since, 1 = 60° and 5 = 60° [from equation (v)],

We can say that these corresponding angles are equal, i.e.,

1 = 5 = 60° - - - - (vi)

Similarly, we get

8 = 4 = 120° (which are also the corresponding angles, and from equation (i), 4 = 120°)

And, 7 = 3 = 60° (which are also the corresponding angles, and from equation (iii), we have 3 = 60°)

Thus, we can say that

l is a transversal intersecting two lines m and n such that each pair of corresponding angles are equal.

Then, lines m and n are parallel to each other.

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