The sides `B A` and `D C` of a quadrilateral `A B C D` are produced as shown in Figure. Prove that `a+b=x+ydot` Figure

Explanation

To prove that \( a + b = x + y \) in the given quadrilateral \( ABCD \) with the sides \( BA \) and \( DC \) produced, we can follow these steps:

### Step 1: Identify the Angles
Let:
- \( \angle BAD = a \)
- \( \angle ABC = b \)
- \( \angle DCA = x \)
- \( \angle BCD = y \)
...