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In the given figure, AB||DE. Prove that:...

In the given figure, `AB||DE`. Prove that:
`angleABC+angleBCD=180^(@)+angleCDE`.

Text Solution

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`CF||BA` and CB is the transversal.
`:. angleABC+angleBCF=180^(@)` ...(i) [co-interior `angles`].
Again, `FC||DE` and DC is the transversal.
`:. angleFCD=angleCDE` ...(ii) [alternate interior `angles`].
Adding the corresponding sides of (i) and (ii), we get
`angleABC+(angleBCF+angleFCD)=180^(@)+angleCDE`.
`implies angleABC+angleBCD=180^(@)+angleCDE`.
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