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In the figure, BA || ED and BC || EF. ...

In the figure, BA `||` ED and BC `||` EF. Show `/_ABC + /_DEF = 180^(@)`.

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Given BA `|""|` ED and BC `|""|` EF.
To show `/_ABC + /_DEF - 180^(@)`.
Construction Draw a ray PE opposite to ray EF.

Proof In the figure, BC`|""|`EF
`:./_EPB + /_PBC = 180^(@)" " `[sum of cointerior angles is`180^(@`] ....(i)
Now, AB`|""|` ED and PE is a transversal line.
`:. " " /_EPB = /_DEF " " [corresponding angles ] ....(ii)`
From Eqs. (i) and (ii), `/_DEF + /_PBC = 180^(@)`
`rArr " "/_ ABC + /_ DEF = 180^(@)" " [:./_PBC - /_ABC]`
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