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This is a geometry problem involving parallel lines and angles in a quadrilateral. Based on the information in the image:

- \( AB \parallel CD \) (AB is parallel to CD)
- \( AC = BD \) (AC is equal to BD)
- \( \angle ADB = 80^\circ \)
- \( \angle CAD = 20^\circ \)

The goal is to find \( \angle ADC \).

### Step-by-step solution:

1. **Use the property of parallel lines**: Since \( AB \parallel CD \), \( \angle CAD \) and \( \angle ADB \) form a pair of alternate angles. Thus, \( \angle ADB = 80^\circ \) implies that the angle adjacent to \( \angle CAD \) at point \( C \), denoted as \( \angle DCA \), is also \( 80^\circ \) (corresponding angle property).

2. **

In the figure, AB is parallel to CD, AC = BD, ∠ADB = 80°, and ∠CAD = 20°. Find ∠ADC.

Learn how to solve for the angle ∠ADC in a geometry problem involving parallel lines, where AB is parallel to CD, and AC = BD. This problem covers key concepts such as corresponding angles and the sum of angles in a triangle. Suitable for students in Grades 8-10.

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