Find the value of in the adjoining figure if AB ∥ CD.
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Answer:Given∠DCE=100
o
&∠ABE=120
o
LetusextendABsuchthatitmeetsCEatF&extendstillG.
GivenAB∥CD,soAG∥CD.LetCEbethetransversal.
Then∠DCE=∠GFE=100
o
[Correspondingangles]
∠ABE+∠EBF=180
o
[Since∠ABFisastraightangle]
⇒∠EBF=180−120=60
o
∠GFE+∠EFB=180
o
[Since∠BFGisastraightangle]
⇒∠EFB=180−100=80
o
Nowin△BFE,
∠EBF+∠EFB+∠FEB=180
o
⇒60+80+x
o
=180
o
⇒x
o
=180−140
⇒x
o
=40
o
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