Since $\stackrel{⟷}{AP}and\stackrel{⟷}{BC}$  are parallel and considering AB as the transversal, we have:

$\angle QAB=\angle ABC=y$   [alternate angles are equal]

A transversal is a line which intersects two (or more) lines in two (or more) distinct points. However, in this case, either of the lines$\stackrel{⟷}{AB}and\stackrel{⟷}{CD}$,  intersect only in one point. Hence, neither of  $\stackrel{⟷}{AB}and\stackrel{⟷}{CD}$, can be a transversal.

Euclid's axiom states that - 'Things which are equal to the same thing are equal to one another'. Hence CD = KA = TP.
Therefore,
KA + TP = CD + CD = 2 CD

 Playfair was a Scottish mathematician who's postulate is a simple equivalent version of the parallel postulate of Euclid. Playfair's postulate states that- ' Given a line in a plane and a point outside the line in the same plane, there is a unique line passing through the given point and parallel to the given line.'

Given any straight line segment, a circle can be drawn having the segment as radius and one endpoint as the centre is the postulate given by Euclid.
A circle cannot be drawn for any given line segment as its diameter and any point on it as the centre.

A theorem is a proposition that has been proved logically on the basis of previously established statements. In total, see the following table:

Interior angle can be defined as:
When two parallel lines are crossed by another line (which is called the transversal), the pairs of angles on opposite sides of the transversal  but inside the two lines are called interior angles.
So in the given question, the interior angles are $\angle$3, $\angle$4, $\angle$5, $\angle$6.

If two lines are parallel then:

Corresponding angles are equal i.e., $\angle a=\angle e$

Alternate interior angles are equal i.e., $\angle c=\angle f$

Alternate exterior angles are equal i.e., $\angle b=\angle g$

Vertically opposite angles are equal in case of intersecting lines.