Final answer:
Using the congruence of angles ABC and PQR and setting the expressions for their corresponding sides equal, we solve for x and find that AB is 8 units and PR is 5 units long.
Step-by-step explanation:
If angle ABC is congruent to angle PQR, then by the Corresponding Parts of Congruent Triangles are Congruent (CPCTC), we know that their sides opposite these angles are also congruent, so AB = PQ and BC = PR.
Given that AB = 8x and PQ = 4x + 4, we can set up the following equation :
8x = 4x + 4
Solving for x gives us:
8x - 4x = 4
4x = 4
x = 1
Now that we have the value of x, we can substitute it back into the expressions for AB and PR to find their lengths :
AB = 8x = 8(1) = 8
PR = 2x + 3 = 2(1) + 3 = 5
Therefore, the length of AB is 8 units and the length of PR is 5 units.