Given that . In , , , and in , . What is the measure of ?

Question Analysis:
This question focuses on applying the concepts of CPCTC (Corresponding Parts of Congruent Triangles are Congruent) and the triangle - angle - sum theorem.
The main task is to first find the value of

by equating corresponding angles and then use the fact that the sum of interior angles of a triangle is

to determine the measure of

.

Key Concept Explanation:
CPCTC states that when two triangles are congruent, their corresponding angles and sides are congruent.
The triangle - angle - sum theorem tells us that the sum of the interior angles of any triangle is always

.
We will use these two principles to solve the problem.

Step - by - Step Solution:
1. Find the value of

:
Since

, then

(by CPCTC).
Set up the equation:

.
Subtract

from both sides:

, which simplifies to

.
Add 10 to both sides:

.
2. Find the measures of

and

:
Substitute

into the expression for

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