Question

In Fig 8.117, p is a transversal to lines m and n, ∠2 = 120° and ∠5 = 60°. Prove that m||n.

Answer 1

m ‖ n (as pair of corresponding angles are equal)

Step-by-step explanation:

Given :  

∠2 = 120° and ∠5 = 60°

 

To prove : m || n  

∠2 + ∠1 = 180° (Linear pair)

120° + ∠1 = 180°

∠1 = 180° – 120°

∠1 = 60°

 

Since,

∠1 = ∠5 = 60° [corresponding angles]

Therefore,

m ‖ n (as pair of corresponding angles are equal)

Extra information :  

Parallel lines:

If two lines lie in the same plane and do not intersect when produced on either side then such lines are said to be parallel to each other.

 

If a transversal intersects two lines such that a pair of corresponding angles is equal then the two lines are parallel.

Hope this answer will help you…..

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Answer 2

Given: ∠2 = 120° and ∠5 = 60°

To prove: m||n

Proof: ∠2=∠4 (vertically opp. ∠'s)

Therefore,

∠4=120°

=>∠4+ ∠5=120°+60°

=> ∠4+ ∠5=180°

=> ∠4 and ∠5 are supplementary angles.

=>Consecutive interior angles are supplementary.

=>m||n