Q44 of 93 Page 6

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

m and n are two lines cut by a transversal l.     ∠ 2 = 120°   ∠ 2 = ∠ 4 (Vertically opposite angles are equal). ∴ ∠ 4 = 120° Adjacent angles, ∠ 3, ∠ 4 form a linear pair. ⇒ ∠ 3 + ∠ 4 = 180° (Linear Pair Axiom)       ∴ ∠ 3 = 180° - ∠ 4                = 180° - 120° ( from (1) )                = 60°    But, ∠ 5 = 60° (given)       ∴ ∠ 3 = ∠ 5 (Alternate interior angles are equal) ∴ m || n.

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