Q. 43

In the figure AB || CD and ∠ECD = 100° and ∠ABE = 110°, find the value of x.

Answer :

Since AB || CD
    ... AF || CD ….(AB was produced to F) and CF is transversal 
... ∠DCF = ∠BFC = 100°
Now ∠BFC + ∠BFE = 180° ….(Linear pair)
   ... 100° + ∠BFE = 180°
              ... ∠BFE = 180° - 100° = 80°
Now in ΔBFE, we have
  ∠ABE = ∠BFE +∠BEF
⇒ 110° = 80° + x°
    Þ x = 110° - 80° = 30°

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