Q81 of 93 Page 6

In figure, prove that p||m.
       

In Δ BCD, ∠ B + ∠ C + ∠ D = 180° [Sum of the angles of a triangle is 180° ]
⇒ ∠ B + 45° + 35° = 180°
                ⇒ ∠ B  = 180° - (45° +35° )
                          = 180° - 80°
             ⇒ ∠ DBC = 100° ………………………..(i)
     ∠ DBE + ∠ DBC = 180° [Linear pair axiom]
    Þ ∠ DBE + 100° = 180° [From (i)]
              Þ ∠ DBE = 180° - 100° = 80°
              ⇒ ∠ DBE = ∠ FAB
But these angles form a pair of corresponding angles when p and m are cut by a transversal n, which are equal.
p || m.

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