The problem involves a geometric figure with some angles labeled, and you are asked to calculate a specific angle.

Given information:

• $AB \parallel CD$
• $AC = BD$
• $\angle ADB = 80^\circ$
• $\angle CAD = 20^\circ$

We need to find the value of $\angle ADC$.

Step-by-step solution:

1. Since $AB \parallel CD$, $\angle ADB = \angle DAC = 80^\circ$ by alternate interior angles.

2. In triangle (