Since line AB and line CD are parallel lines, the measure of angle 5 is equal to 35 degrees.
In Mathematics and Geometry, the alternate interior angles theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent:
By applying the alternate interior angles theorem to the diagonal of quadrilateral ABCD, we can logically deduce the following pair of congruent angles because line AB and line CD are parallel lines;
m∠1 ≅ m∠6
m∠2 ≅ m∠5
In this context, the measure of angle 5 must be equal to 35 degrees;
m∠5 = 35°.