Geometry

Question Analysis:
This question involves applying the ASA Congruence Postulate along with length calculations.
The main focus is on:
Proving triangle congruence using ASA
Using corresponding parts of congruent triangles (CPCTC) to find missing side lengths

Key Concept Explanation:
ASA Congruence: If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent.
CPCTC: Corresponding Parts of Congruent Triangles are Congruent.
Once triangles are congruent, all their corresponding sides and angles are equal.

Step-by-Step Solution:
Check ASA Conditions:
∠A = ∠P = 50° (Given)
∠B = ∠Q = 70° (Given)
Side AB = PQ = 12 cm (Given, included side)
⇒ ΔABC ≅ ΔPQR by ASA Congruence.
Use CPCTC to Find AC:
Since ΔABC ≅ ΔPQR, their corresponding sides are equal.
AC corresponds to PR.
Given ...