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The problem asks us to find \( m\angle C \) in the given triangle \( \triangle ABC \), where:
- \( AC \cong BC \) (meaning triangle \( ABC \) is isosceles),
- \( m\angle A = 80^\circ \).

### Step-by-step solution:

1. **Isosceles Triangle Property**: Since \( AC = BC \), the angles opposite those sides must be equal. Thus, \( \angle A = \angle B \).
   
2. **Sum of Angles in a Triangle**: The sum of all angles in any triangle is \( 180^\circ \). Therefore, 
   \[
   m\angle A + m\angle B + m\angle C = 180^\circ
   \]
   Substituting \( m\angle A = 80^\circ \) and \( m\angle A = m\angle B \), we get:
   \[
   80^\circ + 80^\circ + m\angle C = 180^\circ
  

In the accompanying diagram, AC ≅ BC and m∠A = 80°. Find m∠C.

Learn how to find m∠C in an isosceles triangle where AC ≅ BC and m∠A = 80°. This problem involves the isosceles triangle theorem and the sum of angles in a triangle formula. Suitable for Grades 7-10.

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