Question

In quadrilateral ABCD AB||DC and AD=BC show that angel A=angle B

Answer 1

Let E∈DC such that AE||BC. Thus, AECB is parallelogram,

which gives AE=BC and from here AE=AD.

Thus, ∡ADE=∡AED=∡BCD.

Now,

∡DAB=180∘−∡ADC=180∘−∡BCD=∡ABC