Question

ABCD is an isosceles trapezium with Angle B = 60° and AD ||BC. Side AD is produced till E such that

AE = BC, CE is joined. Find Angle DCE.​

Answer 1

Given-   AD // BC    

             AE = BC

             angle B = 60

According to the question, ABCD is an isosceles trapezium

Therefore AB = CD, hence angle B = angle C and angle A = angle D

Now quadrilateral ABCE is a parallelogram because AB parallel and equal to CE and CB is parallel and equal to AE

Therefore by parallelogram's property which is that opposite angles are equal, we get angle EAB = angle BCE = 120

and angle ABC = angle AEC = 60

Now triangle CDE is an isosceles triangle with CD = CE

Therefore angle CDE = angle CED = 60

By using angle sum property in triangle DCE we get angle DCE = 60

I hope this helped. Please mark my answer as the brainliest!