In Fig, Show that AB ∥ EF.

1.	In Fig, Show that AB ∥ EF.
Answer» We know that, ∠ACD = ∠ACE + ∠ECD ∠ACD = 35° + 22° ∠ACD = 57° = ∠BAC Thus, lines BA and CD are intersected by the line AC such that, ∠ACD = ∠BAC So, the alternate angles are equal Therefore, AB ∥ CD ……1 Now, ∠ECD + ∠CEF = 35° + 45° = 180° This, shows that sum of the angles of the interior angles on the same side of the transversal CE is 180° So, they are supplementary angles Therefore, EF ∥ CD …….2 From equation 1 and 2 We conclude that, AB ∥ EF

Answer»

We know that,

∠ACD = ∠ACE + ∠ECD

∠ACD = 35° + 22°

∠ACD = 57° = ∠BAC

Thus, lines BA and CD are intersected by the line AC such that, ∠ACD = ∠BAC

So, the alternate angles are equal

Therefore, AB ∥ CD ……1

Now,

∠ECD + ∠CEF = 35° + 45° = 180°

This, shows that sum of the angles of the interior angles on the same side of the transversal CE is 180°

So, they are supplementary angles

Therefore, EF ∥ CD …….2

From equation 1 and 2

We conclude that, AB ∥ EF

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