Geometry

Question Analysis:
This question applies the concepts of CPCTC and the triangle - angle - sum theorem.
The main focus is on using the equality of corresponding angles from congruent triangles and the fact that the sum of interior angles in a triangle is to find the value of , and then determine the measure of .

Key Concept Explanation:
CPCTC means corresponding parts of congruent triangles are congruent.
Also, the sum of the interior angles of a triangle is always . We'll use these two concepts to solve the problem.

Step - by - Step Solution:
1. In , by the triangle - angle - sum theorem, , so .
Since , then (by CPCTC).
Given , we set up the equation .
2. Solve the equation for :
   - Add to both sides: , which simplifies to .
   - Subtract 50 from both sides: , so

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