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The given figure shows that two parallel...

The given figure shows that two parallel lines cut by the transversal AB. If `anglea: angleb =4:5`, find the angles a,b,c,d,e and x.

Text Solution

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`anglea+angleb=180^(@)" "` (linear pari )
Also given that `anglea : angleb=4:5`
`:. anglea=(4)/(9)xx180^(@)=80^(@)`
and `angle=(5)/(9)xx180^(@)=100^(@)`
Now, `anglec=anglea=80^(@) " "` (vertically opposite angles)
and `angled=anglec=80^(@)" "` (alternte interior)
and `angle=angleb=100^(@)" "` (corresponding angles )
`anglex+anglee=180^(@) " "` (linear pair)
Therfore, `anglex+100^(@)=180^(@)`
`rArr angle=80^(@)`
Hence , `a=80^(@),b=100^(@),c=80^(@),d=80^(@),e=100^(@),x=80^(@)`
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