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

Question

In Fig 8.117, p is a transversal to lines m and n , &#x2220; 2 = 120&#xB0; and &#x2220; 5 = 60&#xB0;. Prove that m || n .

Philoid · Accepted Answer

Given that,

∠2 = 120^o

∠5 = 60^o

To prove: ∠2 + ∠1 = 180^o(Linear pair)

120^o + ∠1 = 180^o

∠1 = 180^o – 120^o

= 60^o

Since,

∠1 = ∠5 = 60^o

Therefore,

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