In the given figure, AB || CD, ∠BAE = 100° and ∠AEC = 30°. Find ∠DCE.

Since AH || EC

So, ∠GAE = ∠AEC = 30° {alternate angle}

Also ∠BAG = 100°-∠GAE

∠BAG = 70°

Here also, AB || DC and GH acts as transversal.

So, ∠BAG = ∠DHA = 70° {corresponding angles}

Similarly,

AH || EC and DC acts as transversal.

So, ∠DCE = ∠DHA = 70° {corresponding angles}