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In Figure, arms BA and BC of /A B C are ...

In Figure, arms `BA and BC of /_A B C` are respectively parallel to arms `E D` and `E F` of `/_D E Fdot` Prove that `/_A B C+/_D E F=180^@`

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Given: In `/_ABC` and `/_DEF`
`BA ||ED` and `BC || EF`
To prove:`/_ABC + /_DEF = 180^@`
Construction : Produce `BC` to `H` intersecting `ED` at `G`
Proof: `AB || ED`
∴`/_ABC= /_EGH`..(i)(Corresponding angles)
∵`/_EGH + /_DEF =180^@` (Sum of co-interior angles)
⇒`/_ABC+/_DEF = 180^@` [From (i)]
Hence proved.
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