In the figure, ∠1 = 60° and ∠6 = 120°. Show that the lines m and

1.	In the figure, ∠1 = 60° and ∠6 = 120°. Show that the lines m and n are parallel.
Answer» According to the question, We have from the figure ∠1 = 60° and ∠6 = 120° Since, ∠1 = 60° and ∠6 = 120° Here, ∠1 = ∠3 [since they are vertically opposite angles] ∠3 = ∠1 = 60° Now, ∠3 + ∠6 = 60° + 120° ⇒ ∠3 + ∠6 = 180° We know that, If the sum of two interior angles on same side of l is 180°, then the lines are parallel. Therefore, m \|\| n

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

Answer»

According to the question,

We have from the figure ∠1 = 60° and ∠6 = 120°

Since, ∠1 = 60° and ∠6 = 120°

Here, ∠1 = ∠3 [since they are vertically opposite angles]

∠3 = ∠1 = 60°

Now, ∠3 + ∠6 = 60° + 120°

⇒ ∠3 + ∠6 = 180°

We know that,

If the sum of two interior angles on same side of l is 180°, then the lines are parallel.

Therefore, m || n