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The problem involves two congruent triangles, and you are asked to determine the measure of angle \( \angle C \), given that \( \angle E = 45^\circ \) and \( \angle B = 55^\circ \).

Let's break it down:

1. The two triangles are congruent, meaning all corresponding sides and angles are equal. Therefore, \( \triangle ACB \) is congruent to \( \triangle EDC \).

2. In a triangle, the sum of the interior angles is always \( 180^\circ \). For triangle \( \triangle EDC \), we know that \( \angle E = 45^\circ \) and \( \angle B = 55^\circ \).

3. We can calculate \( \angle C \) by using the triangle angle sum theorem:

\[
\angle C = 180^\circ - \angle B - \angle E
\]

Substitute the known values:

\[
\angle C = 180^\circ - 55^\circ - 45^\circ = 80^\circ
\]

Thus, \( \angle C = 80^\circ \).

The correct answer is **80°**.

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Would you like more details or have any questions?

Here are 5 related questions:
1. How do you prove two triangles are congruent?
2. What are the different methods for determining triangle congruence (e.g., SSS, SAS, etc.)?
3. What is the exterior angle theorem for triangles?
4. Can two triangles be congruent if they only have two pairs of equal angles?
5. What are the properties of isosceles triangles?

**Tip:** Always check if triangles are congruent before assuming corresponding angles are equal.

These triangles are congruent. If ∠E = 45° and ∠B = 55°, what is the measure of ∠C?

Explore how to solve for ∠C in a pair of congruent triangles. Using the triangle angle sum theorem, we calculate that ∠C = 80°. This problem covers key geometry concepts and is suitable for students in Grades 8-10.

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