In the given diagram, lines AB and CD are parallel. What is the angle θ ?

Given :- AB and CD are parallel.

Concept used :- We will use the angle sum property.

Solution :- \(\angle BEC=\angle AED=140\)  {Alternate exterior angle}

\(\angle AEB=\angle DEC\) {Alternate interior angles}

\(\angle DEC+\angle DEA+\angle AEB+\angle BEC=360\)

\(\implies \angle AEB=40\)

\(\angle B=\angle D=75\) {Vertically opposite angle}

Hence, using angle sum property

\(\angle A+\angle B+\angle AEB=180\)

\(\angle A=\theta= 180 - (40 + 75) = 180 - 115 = 65\)