In each of the figures given below, `AB||CD`. Find the value of x in each case.

Answer

(i) `x=100` (ii) `x=280` (iii) `x=120`

Explanation

(i) Draw `EF||AB|CD`.
`angleBEF=angleABE=35^(@)` [alt. int. `angles`]
`angleDEF=angleCDE=65^(@)` [alt. int. `angles`].
`:. X^(@)=(angleBEF+angleDEF)=(35^(@)+65^(@))=100^(@)`.

(ii) `AB||EO` and BO is the transversal.
`:. angleABO+angleEOB=180^(@)`
`implies 55^(@) +angleEOB=180^(@) implies angleEOB=125^(@)`.
`CD||EO` and `DO` is the transversal.
`:. angleCDO+angleEOD=180^(@)`
`implies 25^(@)+angleEOD=180^(@) implies angleEOD=155^(@)`
`:. x^(@)=(125^(@)+155^(@))=280^(@)`.

(iii) Draw `EF||AB||CD`.
`angleBAE+angleAEF=180^(@)`
`implies 116^(@)+angleAEF=180^(@) implies angleAEB=64^(@)`.
`angleCEF+angleECD=180^(@) implies angleCEB=(180^(@)-124^(@))=56^(@)`.
`:. x^(@)=(64^(@)+56^(@))=120^(@)`.