Question

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

Answer 1

<GAE =<AEC =30° (alternate  interior angles)
<BAG =100° - 30° =70° 
since AB and CD are parallel,<BAG=<DHA=<DCE=70° (corresponding anles)

Answer 2

Answer:

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}